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A  UTHOR : 


JONES,  EMILY 
ELIZABETH 


riTLE: 


INTRODUCTION  TO 
GENERAL 


PL  4  CI 


LONDON 


DATE: 


1892 


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AN    INTRODUCTION 


TO 


GENERAL    LOGIC 


BY 


E.   E.   CONSTANCE  JONES 

«        r  * 

AUTHOR   OF 
'  ELEMENTS   OF   LOGIC   AS   A  SCIENCE  OF   PROPOSITIONS  ' 


■•n 


LONDON 
LONGMANS,   GREEN;  AND   CO. 

AND  NEW  YORK:  15  EAST  i6th  STREET 

1892 

All  rights  reserved 


i  I 


/*, 


PREFACE. 


i 


i 


r 


Ov 


My  object  in  preparing  this  volume  has  been  to 
provide  a  "  First  Logic  Book  "  which  may  be  used  in 
teaching  beginners,  and  at  the  same  time  furnish  a 
connected,  though  brief,  sketch  of  the  science.  I  am 
aware  that  a  large  number  of  elementary  Text-books 
and  Manuals  of  Logic  have  appeared  in  recent  years ; 
and  my  only  excuse  for  adding  to  the  number  is 
the  hope  I  entertain  that  what  I  have  to  say  may  be 
of  use,  and  may  help  to  remove  certain  difficulties 
which  are  familiar  to  all  teachers  of  Logic,  and  which 
have  been  very  forcibly  pressed  upon  my  attention 
during  an  experience  of  several  years,  in  teaching 
elementary  Logic. 

In  the  present  volume  I  have  attempted  to  set 
forth,  as  simply  and  systematically  as  possible,  views 
indicated  in  a  small  book — substantially  a  collection 
of  Notes  on  difficult  points  in  Logic — which  I  wrote 


14617U 


IV 


PREFACE. 


three  years  ago.     In  that  book  I  discussed  fully  the 
cases  in  which  I  diverge  from  traditional  doctrines, 
and  my  reasons  for  the  divergence ;  and  this  obviates, 
I  hope,  any  necessity  for  introducing  controversial 
matter  in  the  present  work— in  which,  of  course,  it 
would  be  peculiarly  inappropriate.     In  the  former 
book    I    acknowledged    my   obligations    to    various 
thinkers  and  writers,  as  far  as  I  was  definitely  con- 
scious of  them;  but  in  such  matters  it  is  perhaps 
never  possible  to  trace  more  than  a  very  small  part 
of  the  debt  which  one  owes  to  others. 

My  whole  scheme,  as  here  presented,  follows  natur- 
ally from  the  view  taken  of  the  twofold  character  of 
Terms— which,  as  Names  of  Things,  have  both  appli- 
cation and  signification.      On  this  datum,  together 
with  the  recognition  that  things  have  a  plurality  of 
Characteristics  and  a  consequent  plurality  of  Names, 
depends  (I  think)  the  possibility  of  Significant  Asser- 
tion, and  the  whole  doctrine  of  Inference,  Mediate  and 
Immediate.     The  Principle  of  Excluded  Middle  sug- 
gests and  supports  a  recognition  of  the  relatedness  of 
things  to  one  another ;  and  a  consideration  of  Bacon's 
doctrine  oiForm  suggests  a  modification  of  Mill's  view 
of  Induction.     The  relation  of  Induction  to  Deduc- 


f 


PREFACE.  V 

tion  appears  to  me  to  be  so  close  that  it  is  more  con- 
venient to  regard  all  Logic  as  one,  than  to  make  a 
radical  and  fundamental  division  between  Deductive 
(or  '  Formal ')  and  Inductive  (or  '  Material ')  Logic. 
Upon  the  twofold  character  of  Terms,  again,  depends 
the  explicit  recognition  of  the  Law  of  Identity  as  a 
Law  of  Identity  in  Diversity.  And  I  believe  that 
what  I  have  to  say  about  Kelative  Propositions  in 
Section  IV.  and  elsewhere,  about  Quantification  in 
Section  YIL,  the  view  of  Disjunctives  in  Section  VL, 
and  of  the  force  and  interdependence  of  the  Prin- 
ciples of  Logic  in  Section  XIX.,  is  to  some  extent 
new ;  likewise  the  systematisation  of  Fallacies  in 
Section  XVIIL,  and — in  part — the  elaboration  of 
Immediate  Inferences  in  Section  X.  My  view  that 
Logic  is  concerned  with  Assertions  expressed  in  lan- 
guage, and  that  it  is  distinctly  not  a  department  of 
Psychology,  is  not  peculiar  to  me. 

I  have  omitted  from  the  text  any  matters  of  which 
the  interest  is  largely  historical,  or  which  are  not  of 
direct  importance  for  the  theoretical  outline  which  is 
all  that  I  have  attempted  to  give.  But  for  conveni- 
ence of  reference,  a  brief  account  of  such  of  these  as 
are  generally  included  in  elementary  text-books  is 


VI 


PREFACE. 


contained  either  in  the  Notes  which  follow  Section 
XIX.,  or  in  the  Index  and  Vocabulary. 

A  collection  of  Questions  precedes  the  Index. 
They  are  taken  chiefly  from  published  Examination 
Papers  of  the  University  of  Cambridge,  and  a  few  are 
from  Oxford  or  London  Examination  Papers.  A  con- 
siderable number,  however,  are  extracted  from  pub- 
lished works  of  the  late  Professor  Jevons.  These  are 
marked  with  a  (J) ;  and  those  from  Cambridge,  Oxford, 
or  London  papers  with  (C),  (0),  or  (L)  respectively. 
The  Table  of  Contents  is  intended  to  furnish  a  com- 
plete summary  of  the  text. 

I  wish  to  express  my  sincere  thanks  to  Professor 
Caldecott,  M.A.,  of  King's  College,  London,  and  of  St. 
John's  College,  Cambridge,  for  his  kindness  in  read- 
ing the  proofs  of  this  book,  and  for  nuich  valuable 
criticism.  I  am  also  indebted  for  several  suggestions 
to  Miss  Alice  Gardner  and  Miss  E.  Rhodes,  both  of 
Newnham  College,  Cambridge. 

GiRTON  College,  Cambridge, 
March  24th,  1892. 


CONTENTS. 


PART  I. 

IMPORT  OF  PROPOSITIONS. 
SECTION  I. 

DEFINITION  AND  SCOPE  OF  LOGIC. 

All  knowledge  is  contained  in  Statements  or  Propositions. 
The  only  method  of  explaining,  questioning,  justifying,  or 
disproving  any  Proposition  is  by  means  of  other  Proposi- 
tions  having  some  relation  to  it.  Logic  may  be  called  the 
Science  of  the  Import  and  Relations  of  Propositions;  and 
since  all  Sciences  are  expressed  in  Propositions,  Logic  is 
thus  the  Science  of  Sciences— that  is,  the  Science  of  a 
method  of  procedure  which  applies  in  every  department 
of  knowledge.  General  Logic  starts  from  the  standpoint 
of  ordinary  thought,  and  assumes  Reason  in  Man  and 
Trustworthiness  in  Language, 

SECTION  II. 
ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 

A  Proposition  is  an  assertion  expressed  in  words,  and 
Propositions  may  be  primarily  divided  into  Categorical, 
Conditional,  Hypothetical,  and  Alternative.  A  Cate- 
gorical Proposition  consists  of  two  Terms  (Subject 
and  Predicate)  and  a  Copula.  Terms  are  primarily 
Names,  and  a  Name  is  a  word  or  combination  of  words 
applying  to  some  thing  or  group  of  things,  and  signifying 
some  characteristics  of  that  to  which  it  applies.     Apph- 


PAGE 


1-3 


vu 


Vm  CONTENTS. 

cation  and  Signification  of  names  correspond  to  Existence 
and  Character  in  the  things   named.     Names  may  be 
divided  into  (1)  Substantive  Names,  (2)  Attribute  Names, 
(3)  Adjectival  Names:   (1)  being  further  divided  into 
Common,  Special,  Proper,  and  Unique.   (1)  and  (2)  may  be 
either  Subjects  or  Predicates  of  Propositions,  but  Adjec- 
tives can  be  Predicates  only,  and  can  be  predicated  of 
either  (1)  or  (2),  whereas  (1)  and  (2)  cannot  be  predicated 
of  each  other.    Proper  Names  afford  in  themselves  no 
guidance  whatever  for  their  own   application  in   fresh 
cases.     A  Term  is  any  word  or  combination  of  words 
applying  to  that  of  which  something  is  asserted  (Subject), 
or  to  that  which  is  asserted  of  it  (Predicate).     Term  must 
be  distinguished  from  Tei-m-name.    Many  of  the  most  im- 
portant distinctions  in  Propositions  depend  upon  diflfer- 
ences  in  the  Terms,   especially  in   the  Subject-Terms. 
Still  the  characteristics  of  Terms  often  cannot  be  settled 
without  reference  to  the  Propositions  of  which  they  are 
Terms.     The  widest  distinction  between  Terms  is  that 
between  Uni-terminal  or]Adjectival  Terms  (Terms  which 
can  only  be  used  as  Predicates  of  Propositions) ;  and  Bi- 
terminal  Terms  (Terms  which  may  be  used  both  as  Sub- 
jects and  Predicates).     To  this  distinction  there  corre- 
sponds a  division  of  Propositions  into  Coincidental  and 
Adjectival.    The  principal  division  of  Bi- terminal  Terms 
is  into  Attribute  Terms  and  Substantive  Terms.    Among 
the  further  subdivisions  of  Terms,  a  specially  important 
one  is  that  into  Absolute  and  Relative  (implying  a  de- 
pendence or  relation  of  Subjects  of  Attributes  connected 
in  some  system,  which  may  be  of  any  degree  of  com- 
plexity, from  the  simplicity  of  a  class  or  of  any  two  re- 
lated objects  to  the  intricacy  of  a  genealogical  tree,  or 
even  of  the  Universe  itself).     From  a  Relativ^e  Proposi- 
tion— i.e.  a  Proposition  containing  a  Relative  Term  {e.g. 
E  is  equal  to  F), — far  more  immediate  inferences  can  be 
drawn  than  can  be  drawn  from  an  Absolute  Proposition. 
Mathematical  Propositions  are  a  specially  important  case 
of  Relative  Propositions.     The  Copula  may  be  affirmative 
or  negative.    Its  office  is  to  express  a  certain  relation  be- 
tween the  Terms,      ........ 

Tables  of  Names  and  TerniH, 


PAGE 


J 


I 


4-17 
18,19 


CONTENTS. 

SECTION  III. 

CATEGORICAL  PROPOSITIONS  AS  WHOLES. 

A  Categorical  Proposition  may  be  defined  as  a  Proposition 
ivhich  asserts  Identity  {or  Otherness)  of  Application  in 
Diversity  of  Signification.  This  definition  may  be  made 
clear  and  enforced  by  examples.  Relations  of  Terms  (1) 
must  be  distinguished  from  Relations  of  Classes  (2) ;  (1) 
is  two-fold,  while  (2)  is  five-fold.  The  form  A  is  A  is 
strictly  unmeaning.  In  any  Categorical  Proposition, 
Application  is  prominent  in  the  Subject,  and  Signifi- 
cation is  prominent  in  the  Predicate.  Categorical  Pro- 
positions may  be  subdivided  into  Classes,   which  are 

enumerated  and  illustrated, 

Table  of  Categorical  Propositions,   .... 

SECTION  IV. 

RELATIVE  CATEGORICAL  PROPOSITIONS. 

The  characteristic  which  distinguishes  Relative  Propositions 
from  Absolute  Propositions  is  this  : — In  Relative  Pro- 
positions—such as,  D  /is/  equal  to  F,  A  /is/  like  B— of  the 
two  Terms  (S  and  P)  one  applies  to  some  thing  or  group 
of  things,  and  the  other  expresses  the  relation  of  that  thiiuj 
or  group  to  a  second  thing  or  group.  Hence  it  is  possible 
for  a  person  knowing  the  system  of  things  referred  to,  to 
draw  more  inferences  from  Relative  than  from  Absolute 
Propositions.  A  fortiori  and  other  Relative  Arguments 
can  be  expressed  in  syllogistic  form.  Mathematical  Pro- 
positions are  among  the  most  important  of  Relative  Pro- 
positions. The  Copula  =  in  Mathematical  Propositions  is 
to  be  understood  as  meaning  is  equal  to  {i.e.  is  exactly 
similar  quantitatively)  ;  and  since  a  thing  cannot  be  said 
to  be  equal  to  itself  the  terms  of  Mathematical  Proposi- 
tions (taking  =  as  the  copula)  must  have  different  Appli- 
cations, i.e.  they  must  apply  to  things  numerically 
distinct.  Hence  the  terms  of  Mathematical  Propositions 
can  be  quantified  with  any  only  when  they  have  the  most 
abstract  application  possible— ?.e.  when  they  apply  to 
numbers  generally,  and  are  not  understood  to  refer  to 
some  assigned  unit,  ....••• 


IX 


PAGE 


20-32 
33 


34-41 


CONTENTS. 


SECTION  V. 


INFERENTIAL  PROPOSITIONS. 


PAGE 


An  Inferential  Proposition  is  a  Proposition  of  the  form,  If 
A,  then  C;  and  expresses  a  relation  between  Antece- 
dent and  Consequent  such  that  an  identity  (or  identities) 
expressed  or  indicated  by  the  Consequent  is  an  inference 
from  an  identity  (or  identities)  expressed  or  indicated 
by  the  Antecedent.  Inferential  Propositions  may  be  (1) 
Hypothetical  or  (2)  Conditional.  A  Hypothetical  Pro- 
position is  one  in  which  tv/o  (expressed  or  indicated) 
Categoricals  (or  combinations  of  Categoricals)  are  put 
together  in  such  a  way  as  to  express  that  one  (Con- 
sequent) is  an  inference  from  the  other  (Antecedent). 
A  Conditional  Proposition  is  one  which  asserts  that 
any  object  which  is  indicated  by  a  given  class-name 
and  distinguished  in  some  particular  way,  may  be  in- 
ferred to  have  also  some  further  distinction.  The  im- 
port of  an  Inferential  may  be  expressed  in  a  Categorical 
of  the  form,  G  is  an  inference  from  A.  Hypotheticals 
are  either  Self-contained  or  Referential,  Conditionals  are 
either  Divisional  or  Quasi-Divisional,       ....    42-50 

Table  of  Inftre)itial  Propositions,       ....         51 


SECTION  VI. 

ALTERNATIVE  (OR  DISJUNCTIVE)  PROPOSITIONS. 

Alternative  Propositions  are  of  the  form  Not-C  or  A. 
Alternatives  may  have  some  element  of  unexclusive- 
ness,  but  must  also  have  some  element  of  exclusive- 
ness,  otherwise  there  is  no  Alternation.  In  as  far  as 
*  Alternatives  '  are  absolutely  unexclusive,  they  are  of  the 
form  A  or  A.  Where  Alternatives  are  Propositions, 
there  must  be  some  difference  of  meaning  in  the  Proposi- 
tions (or  there  is  no  Alternation),  and  so  far  there  is  ex- 
clusiveness  ;  but  Alternatives  may  be  true  together,  and 
so  far  there  is  unexclusiveness.  Where  Alternatives  are 
Terms,  there  may  be  unexclusiveness  of  Application, 


CONTENTS. 


XI 


PAGE 


but  there  must  be  some  exclusiveness  of  Signification. 
An  Alternative  Proposition  may  be  defined  as  a  Proposi- 
tion in  which  a  plurality  of  differing  elements  (connected 
by  or  and  called  the  Alternatives)  are  so  related  that  not 
all  of  them  can  be  denied,  because  the  denial  of  some 
justifies  the  assertion  of  the  rest.  Alternative  Proposi- 
tions may  be  Conditional,  Formal,  Subsumptional,  or 

Contingent,       - ^2-56 

Table  of  Alternative  Propositions^      ....         57 


SECTION  VII. 

QUANTIFICATION  AND  CONVERSION,  AND  THE  MEANING 

OF  SOME,  ETC. 

By  Quantification  is  meant  the  introduction  of  some  adjective 
of  quantity  (generally  All  or  Some)  before  the  Predicate- 
Name  in  cases  where  that  Name  is  a  Class-name.     It  is 
not  the  case  that  all  Predicates  are  naturally  quantified 
in  thought,   and   ought  to   be   explicitly  quantified  in 
speech  ;  but  Quantification  is  a  necessary  stage  in  the 
conversion  of  Class  Categoricals.     It  is  only  Coinciden- 
tals  that  can  be  quantificated  and  converted.     From  the 
view  of  the  Import  of   Categoricals  advocated  in  Sec- 
tion III.,  it  follows  that  the  Quantification  of  common 
Categoricals  is  always  possible,  but  is  only  to  be  admitted 
as  a  transformation  stage.     This  view  of  Quantification 
is  confirmed  by  a  consideration  of  the  traditional  logical 
treatment   of   0   Propositions.      The   special   force  and 
meaning  of  Propositions  in  the  stage  of  Quantification 
depends   principally  upon  the  meaning  given  to  Sorne. 
To  define  Some  as  meaning  '  some  but  not  all,'  or  '  some 
at  least,  it  may  be  all,'  or  'not  none,'  is  not  satisfactory. 
It  seems  best  to  say  that  So77ie  E  means  an  indefinite 
quantity  or  number  of  R.     Taking  this  meaning  of  Some, 
Quantification   by   Some   merely  makes   our  Terms  ex- 
pUcitly  indeterminate,  and  the   function  of  Quantifica- 
tion, on  the  whole,  seems  to  be  simply  to  briiuj  into  pro- 
minence the  Application  aspect  oi  ih^Vreiiic^ie,       .         .   58-71 


Xll 


CONTENTS. 


PART  11. 


RELATIONS  OF  PROPOSITIONS. 


SECTION  VIII. 


GENERAL  REMARKS  ON  THE  RELATIONS  OF  PROPOSITIONS. 


Propositions  may  be  related  to  each  other  as  Compatible 
or  Incompatible.  Compatible  Propositions  may  be 
Attached  or  Unattached  ;  and  Attached  Propositions 
may  be  Correlative  or  Premissal,  or  Sub-contrary,  or 
Argumental,  or  Classitic.  There  may  exist  between 
Propositions  relations  which  are  not  apparent  on  mere 
inspection  ;  but  Propositions  ought  not  to  be  connected 
by  Conjunctions,  unless  (1)  they  are  really  related,  (2) 
there  is  some  End  or  Purpose  to  be  subserved  by  show- 
ing their  connection,         ....... 

Table  of  Relations  of  Propositioni<,     .... 


SECTION  IX. 

INFERENCES  IN  GENERAL. 

One  Proposition  is  an  Inference  from  another,  or  others,  when 
the  assertion  of  the  former  is  justified  by  the  latter,  and 
the  latter  is  in  some  respect  different  from  the  former. 
Inferences  may  be  Immediate  (from  one  Proposition 
to  another),  or  Mediate  (from  tivo  Propositions  taken 
together  to  a  third).  Mediate  Inferences  (or  Arguments) 
may  be  Relative  or  Absolute.  All  Absolute  Arguments 
are  Formal,  and  may  be  classed  together  as  Syllogisms. 
Arguments  may  be  Deductive  or  Inductive.  Mediate 
Inferences  differ  from  Immediate  Inferences  only  in 
being  more  complex, 

Table  of  Inferences, 


PAGE 


72-77 
78 


79-86 

87 


CONTENTS. 


xm 


SECTION  X. 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


PAGE 


When  we  pass  from  one  Proposition  to  another,  and  the  latter 
is  justified  by  the  former,  and  differs  from  it  in  some  re- 
spect, the  latter  is  an  Immediate  Inference  (Eduction) 
from  the  former.     Eductions  may  have  (I.)  Categoricals 
(a),  or  Inferential  (6),  or  Alternatives  (c),  for  both  Educt 
or  Educend ;   these  may  be  called  Pure  Eductions  or 
Eversions— or  (II.)  they  may  have  a  Categorical  with  an 
Inferential  (a),  or  a  Categorical  with  an  Alternative  (?>), 
or  an  Inferential  with  an  Alternative  (c).     These  (II.) 
may  be  called  Mixed  Eductions  or  Trans  versions.    There 
are  eight  principal  kinds  of  Eversions  (r/.  Table  viii.). 
In  Transversion  the  most  interesting  points  are  that  all 
Inferentials  and  Alternatives  may  have  their  meaning 
expressed  in  Categorical  form  ;  that  Conditionals   and 
Categoricals  (of  which  S  and  P  in  the  one  correspond  to 
A  and  G  in  the  other)  are  reciprocally  educible  ;   that 
Inferentials  are  educible  from  Alternatives,  and  Alterna- 
tives from  Inferentials,  and  thus  the  Alternative  answer- 
ing to  any  Inferential  has  a  corresponding  Categorical, 
educible  from  the  Categorical  which   answers  to  the 

Inferential, 

Table  of  Immediate  Inferences, l^/ 


SECTION  XI. 

INCOMPATIBLE  PROPOSITIONS. 

Propositions  are  Incompatible  when  they  cannot  both  be 
true.  When  two  Propositions  are  Contrary  they  cannot 
both  be  true  but  may  both  be  false  ;  when  they  are  Con- 
tradictory they  cannot  both  be  true  and  cannot  both  be 
false.  The  relations  of  Classes  and  of  Antecedent  and 
Consequent  may  conveniently  be  illustrated  by  circular 


diagrams. 


108-113 


XIV 


CONTENTS. 


SECTION  XII. 

CATEGORICAL  MEDIATE  INFERENCES. 

In  Mediate  Inferences,  or  Arguments,  the  Inference  is  drawn 
from  two  Propositions  taken  together,  which  are  called 
the  Premisses.  In  Categorical  Mediate  Inferences  the 
Conclusion  and  both  Premisses  are  Categorical  Proposi- 
tions. Categorical  Mediate  Inferences  may  be  divided 
into  Absolute  Arguments  or  Syllogisms,  and  Relative 
Arguments.  A  Categorical  Argument  may  be  defined 
as  a  combination  of  three  Categorical  Propositions,  one 
of  which  (the  Conclusion)  is  inferred  from  the  other  two 
taken  together — these  two  being  called  the  Premisses. 
A  Categorical  Syllogism  is— A  Categorical  Argunient  of 
which  the  Premisses  have  in  common  one  Term-name 
which  does  not  occur  in  the  Conclusion.  The  Conclusion 
has  its  Subject-name  in  common  with  one  Premiss,  and 
its  Predicate-name  in  common  with  the  other  Premiss. 
— The  Canon  of  Categorical  Syllogisms  may  be  stated 
thus  : — If  the  application  of  two  Terms  is  identical  (or 
distinct),  any  third  Term  which  has  a  dififerent  Term- 
name,  and  is  identical  in  application  with  the  whole  (or 
part)  of  one  of  those  two,  is  also  (in  whole  or  part) 
identical  with  the  other  (or  distinct  from  it). — The 
necessary  safeguards  for  the  application  of  the  Canon 
may  be  summed  up  in  three  rules,  of  which  I.  and  II. 
secure  that  there  shall  be  a  true  Middle  Term,  and  no 
illicit  process  of  Major  or  Minor  Term,  and  the  third 
requires  that  a  Negative  Premiss  and  a  Negative  Con- 
clusion shall  always  accompany  each  other.  In  Quanti- 
ficated  Categorical  Syllogisms  and  certain  other  Deduc- 
tions, it  does  not  matter  which  Premiss  is  Major  or  Minor, 
nor  which  Term  is  Subject  and  which  Predicate  in  any  of 
the  three  constituent  propositions.  But  in  dealing  with 
unquantificated  Class  Categoricals  both  these  points 
are  important — hence  the  necessity  of  considering  the 
differences  of  Mood  and  Figure.  By  Mood  is  meant  the 
form  and  order  of  Propositions  which  go  to  make  up  a 


CONTENTS. 


XV 


P    OE 


Syllogism ;  by  Figure  is  meant  the  order  of  Terms  in 
the  Premisses  of  a  Syllogism.     There  are  four  Figures  of 
Syllogism,  called  respectively  the  1st,  2nd,  3rd,  and  4th 
Figures  ;  and  nineteen  valid  Moods  (not  counting  the 
Moods  in  which  there  is  a  weakened  Conclusion).     The 
First  Figure  has  been  regarded  as  the  most  perfect, 
because  to  it,  and  to  it  alone,  the  Aristotelian  Canon  of 
Syllogism  (the  so-called  Dictum  de  omni  et  nullo)  applies 
directly.     Hence  arose  the  doctrine  of  Reduction— that 
is,  of  the  transformation  of  Figures  2,  3,  and  4  to  Figure 
1.     Full  directions  for  Reduction  are  infolded  in  the 
ancient  mnemonic  verse  'Barbara,  Gelarent,'  etc. — Rela- 
tive Categorical  Arguments  are  Arguments  of  which  the 
Premisses  are  Relative  Propositions— they  do  not,  like 
Syllogisms,  conform  to  one  strict  and  invariable  pattern, 
and  the  Canon  and  Rules  of  Syllogism  will  not  apply 
directly  to  them— but  their  cogency  (to  any  one  who 
understands  the  relations  of  the  System  they  refer  to)  is 
just  as  evident  as  that  of  Syllogistic  or  Absolute  Argu- 
ment ;  and  it  is  possible  to  express  them  in  Syllogistic 
form.     It  does  not  seem  possible  to  frame  a  more  precise 
Canon  of  Relative  Categorical  Mediate  Inferences  than 
the  following  :— If  two  objects,  A  and  B,  are  related  to 
each  other,  and  B  is  related  to  a  third  object,  C  ;  then  A 
is  related  to  C  in  accordance  with  the  laws  of  the  system 
to  which  A  and  B  and  C  belong,      ....         114-132 


SECTION    XIII. 


INDUCTIONS. 


Inductive  Inferences  are  Mediate,  and  they  differ  from 
Deductions  in  this,  that  they  consist  of  one  Universal 
and  one  Particular  Premiss,  and  a  Universal  Conclusion. 
In  an  Induction  we  arrive,  by  the  help  of  facts  or  par- 
ticulars, at  some  fresh  generalisation  or  law.  All  Induc- 
tions are  based  upon  the  Principle  that  every  phenomenon 
is  inseparable  from  some  other  phenomena,  and  that  there 
is    uniformity  of  interdependence  between  phenomena. 


"''"''''-^■'^''•^'ntMimiiiiitirfflll^^^ 


CONTENTS. 


XVI  CONTENTS. 

Since  Interdependents  may  be  related  either  as  Concomi- 
tants or  as  Cause  and  Effect,  the  Principle  of  Inter- 
dependence may  be  amplified  as  follows  : — Every  charac- 
teristic of  an  object  has  some  Concomitants,  and  every 
change  or  event  has  some  Cause  and  some  Effect  ;  more- 
over, not  only  is  there  this  connection  in  any  given  case, 
but  the  connection  is  uniform — that  is,  not  only  must 
every  characteristic  have  some  Concomitants,  and  not  only 
must  every  event  have  so7ne  Cause  and  some  Effect,  but 
phenomena  that  are  once  connected  as  Concomitants,  or 
as  Cause  and  Effect,  are  always  so  connected.  And  Uni- 
formity of  Causation  must  depend  upon  Uniformity  of 
Concomitance — our  power  of  predicting  that  one  event, 
A,  will  be  followed  by  another  event,  B,  must  depend 
wholly  upon  co-existence  of  characteristics  in  the  Subjects 
concerned — event  meaning  change  in  Subjects  of  Attributes. 
And  it  seems  further  that  not  only  is  every  characteristic 
invariably  accompanied  by  a  certain  other  characteristic, 
as  Bacon  surmised,  but  also  that  every  kind  of  charac- 
teristic is  one  of  an  unique  group  with  which  it  is 
invariably  and  inseparably  connected.  The  form  of  the 
Principle  of  Interdependence  by  which  we  are  guided  in 
practice  is  the  maxim  that  If  anything,  X,  is  like  another 
thing,  Y,  in  one  respect,  it  is  like  it  in  a  plurality  of 
respects.  But  in  order  to  apply  the  maxim  so  as  to 
arrive  at  an  Induction  in  any  given  case,  we  need  not 
only  to  know  that  similar  phenomena  have  similar 
accompaniments,  but  also  to  know  ivhat^  in  that  case, 
those  accompaniments  are.  It  is  at  this  point  that  the 
*  Inductive  Methods  '  help  us.  The  result  of  an  applica- 
tion of  any  of  those  Methods  is  the  establishment  of  an 
interdependence  between  given  phenomena  in  some 
case  or  cases.  The  assumptions  upon  which  reliance  is 
placed  in  reasoning  by  the  Inductive  Methods  may  be 
summed  up  as  follows  : — If  A  has  never  been  found 
without  B  [norB  without  A] — [Method  of  Agreement  [in 
Presence  and  Absence']) ; — or  if  the  introduction  of  A  is 
followed  by  the  appearance  of  B,  or  the  removal  of  A 
by  the  disappearance  of  B  {Method  of  Difference) ;  or  if 
variation  of  the  quantity  of  A  is  accompanied  or  fol- 
lowed  by  variation   in   the  quantity  of   B  {Method  of 


XVll 


PAGE 


Concomitant  Variations) ;   or  if  in  any  clearly  marked- 
off  set  of  attributes  or  events  AC -BE,  C  and  E  are 
interdependent  {Method  of  Residues)— thQU  A  and  B  are 
interdependent.  —In  an  Inductive  Argument  by  Analogy, 
the  interdependence  that  we  rely  upon  is  inferred  from 
the  complexity  or  amount  of  interdependence  already 
known  or  supposed.     The  reason  why  we  never  use, 
nor  need  to  use,  the  Inductive  Methods  in  the  case  of 
Mathematical  Inductions,   is  that  in  these  cases    the 
inseparability  of  characteristics  is  a  matter  of  direct  per- 
ception :  to  this  reason  is  due  also  the  peculiar  certainty 
which  is  attributed  to   Mathematical  Generalisations. 
The  Principle  of  Interdependence  involves  the  axioms 
that  (1)  No  two  things  are  alike  in  one  respect  only, 
and    (2)    No    thing    is    unlike    another    thing    in    one 
respect  only,  nor  can  any  thing  change  in  one  respect 
only.      To  this  we  may  add  that,   (3)  No  two  things 
are    alike    in   all    respects;     (4)    No    twp    things    are 
unlike  in  all  respects.     (1)  and  (2)   may  be  summed 
up  for  practical  guidance  in  the  maxim,  Apparent  like- 
ness, unlikeness,  or  alteration  is  accompanied  by  non- 
apparent  likeness,  unlikeness,  or  alteration.— Induction 
requires  perception  or  recognition  of  the  Universiil  in  the 
Particular.     In  this  there  are  three  aspects  or  sttkges  :— 
(1)  Hypothesis  ;  (2)  Justification  of  Hypothesis  (generally 
equivalent  to  proof  of  Interdependence) ;  (3)  Extension 
from  the  known  case(s)  to  unknown  cases — a  recognition 
that  the  particular  interdependence  involves  a  connection 
holding  universally.    The  assumptions  which  seem  indis- 
pensable to  Induction  may  be  justified  by  the  considera- 
tion that  they  are  indispensable— that  they  are  involved 
in  the  inductions  which  we  are  continually  making,  and 
on  which  we  unhesitatingly  depend.     If  we  accept  the 
Inductions,  we  must  in  consistency  accept  the  principles 
which  they  involve.      And  if  we  do  not  accept  the 
Inductions,   we  are    entangled  in  a  web  of    hopeless 
inconsistencies.     Further,  in  Section  xix.  we  shall  see 
how  nearly  the  Principle  of  Induction  is  on  the  same 
footing    as    the    Principle    of    Significant    Categorical 
Assertion, 133-149 


sttskmaamB 


MJMmafiaaatt-'---^-''  -'■"-"iJiiifiiiliiW- 


XVlll 


CONTENTS. 


SECTION    XIV. 


INFERENTIAL   MEDIATE   INFERENCES. 


PACK 


An  Inferential  Mediate  Inference  (or  Argument)  consists  of 
Inferential,  or  of  Inferential  and  Categorical  Proposi- 
tions. A  Pure  Inferential  Argument  (1)  consists  of 
three  Inferential  Propositions ;  a  Mixed  Inferential 
Argument  (2)  has  an  Inferential  Major  Premiss  and  a 
Categorical  Minor  and  Conclusion.  (1)  may  be  Hypo- 
thetical (a),  or  Conditional  (h) ;  (2)  may  be  Hypothetico- 
Categorical  (c),  or  Conditio-Categorical  {d).  There  are  ^ 
separate  Canons  for  (a),  (6),  (f),  and  ((Z),  .         .         150-151 

Table  of  Inferential  Syllo(jismft,  ....       152 

SECTION  XV. 
ALTERNATIVE   (OR  DISJUNCTIVE)   MEDIATE  INFERENCES. 

An  Alternative  Mediate  Inference  is  an  Argument  of  which 
one  Premiss  is  always  an  Alternative  Proposition  or  a 
combination  of  Alternative  Propositions,  and  of  which 
one  Premiss  and  the  Conclusion,  or  both  Premisses,  or 
both  Premisses  and  the  Conclusion,  may  be  Alternative. 
Alternative  Arguments  may  be  Pure  (a),  or  Mixed ; 
and  Mixed  subdivide  into  Categorico- Alternative  {b), 
Hypothetico-Alternative  (c),  and  Conditio-Alternative 
(d).      The    four    classes   (a),  {b),  (c),  {d)  have   distinct^ 

Canons, 153-155 

Table  of  A  Ittrnativt  Syllogisms,  .       lo6 

SECTION  XVI. 
DIVISION,    CLASSIFICATION,   AND   SYSTEMATISATION. 

As  regards  Method  generally,  it  may  be  laid  down  that,  in 
any  case,  the  end  in  view  should  not  be  lost  sight  of  : 
that  tautology,  obscurity,  inconsistency,  and  irrelevancy 
should  be  avoided ;  that  the  relations  of  the  parts  of  a 
subject  should  be  plainly  set  forth ;  and  that  the  pro- 
])ositions  which  are  accepted  as  fundamental  should  be 


CONTENTS. 


XIX 


PAGE 


themselves  either  self-evident  or  inferences  from  other 
propositions  which  are  self-evident.  There  are  other 
conditions  of  a  satisfactory  choice  and  articulation  of 
material,  but  they  are  not  easily  reducible  to  rule. 
Classification  should  be  distinguished  from  Classing,  which 
has  a  close  connection  with  Definition.  Classing  consists 
in  grouping  together  a  number  of  numerically  distinct 
objects  in  virtue  of  their  possession  of  similar  character- 
istics, these  characteristics  being  those  which  are  unfolded 
in  the  Definition  of  the  Class-name.  In  Classification  we 
are  concerned  with  the  relations  of  a  number  of  cla^sses, 
the  objects  composing  those  classes  being  regarded  as 
members  of  a  system  of  individuals.  The  function  of  a 
Classification  or  Systematisation  is  to  bring  out  the  Unity 
in  Difference  which  belongs  to  any  group  of  related 
things — Classification  and  Division  are  the  same  thing 
looked  at  from  different  points  of  view.  A  Division 
starts  with  unity  and  differentiates  it ;  a  Classification 
starts  with  multiplicity  and  reduces  it  to  order.  A  good 
Division  or  Cla&sification  should  be  appropriate  to  the 
purpose  in  hand  ;  co-ordinate  classes  should  never  over- 
lap ;  and  at  every  stage  of  a  Division  or  Classification 
the  co-ordinate  classes  should  be  identical  in  extension 
with  the  co-ordinate  classes  of  every  other  stage,  and 
with  the  Summum  Genus.  From  Classing  and  Classifica- 
tion we  may  distinguish  Systematisation — the  arrangement 
of  the  differing  parts  of  a  whole  (whether  single  objects 
or  groups  of  objects)  in  their  relations  to  each  other  and 
to  the  whole.  A  Systematisation  may  often  include 
Classifications, .         157-162 

SECTION  XVII. 

DEFINITION   AND  LANGUAGE. 

By  the  Definition  of  any  word  is  meant  a  Statement  of  the 
Meaning  or  Signification  of  the  word — that  is,  a  Statement 
of  the  characteristics  on  account  ofivhich  ice  apply  the  name, 
and  in  the  absence  of  any  of  ivhich  we  should  not  apply 
it.  Every  name  is  capable  of  being  defined  if  we  include 
the  characteristic  of  being  called  by  the  name  among  those 
characteristics  of  a  thing  which  are  comprised  in  the 


tJAetmiUK^MMsit 


jfctatewiaftj*!wa>aih<ii<iiit».iiniiiiM  "^rfr'a 


XX 


CONTENTS. 


PAGE 


Signification  of  its  name.     But  a  Definition  of  the  kind 
of  Term  which  is  called  a  Proper  Name  is  not  valuable, 
since  in  this  case  Definition  can  never  suffice  as  a  guide 
to  the  first  reference  of  a  name  to  its  object,  nor  can 
knowledge    of  the   reference  of  a  given  name  in  one 
instance  ever  be  a  guide  to  its  reference  in  any  other 
instance.      A    Defiuition   should  be    expressed    m   Ian- 
criiage  that  is  ckar,  simple,  not  tautologous,  and  also 
Ixi    possible)  affirmative  ;    the   word   defined    and    the 
Definition   of   it  must  have  identical    application,    and 
the  Definition  must  state  the  characteristics  included  in  the 
Signification  and  those  only.   The  most  important  Defini- 
tions are  those  of  Class-Names,  and  Classing  has  a  close 
connection   with   Definition,  since  Classing  consists   in 
grouping  together  a  number  of  numerically  distinct  objects 
in  virtue  of  their  possessing  similar  characteristics,  while 
those  characteristics  constitute  the  Signification,  and  this 
is  unfolded  in  the  Definition.     And  both  Classing  and 
Definition    are    connected    with    Induction,   for    Class- 
Names  may  be  regarded  as  a  result  of  Induction,  and 
every    fresh    Induction    that    is    summed    up    in     the 
Signification  of  a  Class-Name  may  be  expressed  in  the 
Definition  of  the  name.     But  the  ultimate  and  supreme 
difficulty  in  Definition  is  to  determine  Signification.    The 
difficulty  arises  from  the  fact  that  all  objects  have  a  vast 
multiplicity  of  properties  (among  which  are  to  be  reckoned 
likenesses  and  uulikenesses  to  other  things) ;  and  since 
no  Definition  could  state  all  the  characteristics  possessed 
in  common  by  any  collection  of  objects,  a  choice  must  be 
made  from  among  many  possible  groups  of  characteristics. 
This  choice  ought  to  be  primarily  determined   by  its 
appropriateness  to  the  purpose  in  hand  ;  it  ought  also  to 
be  as  far  as  possible  conformable  to  usage,  and  at  the 
same  time  consistent ;  and,  finally,  the  characteristics 
selected  ought  to  be  impressive  and  distinctive.      The 
force  of  any  word  as  used  in  Assertion  depends  largely 
upon  context,  including  the  unique  context  which  may 
accompany  it  in  an  individual  mind.     But  the  idea  cor- 
responding to  any  word  must  be  in  some  respects  similar 
in  the  minds  of  all  those  who  understand  its  Application 
and  Signification, 163-177 


CONTENTS. 


XXI 


SECTION    XVIII. 


FALLACIES. 


PAGE 


Confusion  should  be  regarded  not  as  itself  Fallacy,  but  as  a 
source  of  Fallacy.  All  Fallacy  consists  (1)  in  identifying 
what  is  diff'erent,  or  (2)  in  differencing  what  is  identical ; 
thus  we  get  a  primary  subdivision  of  Fallacies  into  those 
of  (1)  professed  Identification,  or  Discontinuity  ;  (2)  pro- 
fessed Difference,  or  Tautology.  Under  these  heads 
Fallacies  of  Definition,  Division,  and  Classification  may 
be  brought  quite  naturally.  Fallacy  may  be  defined  as 
the  assertion  or  assumption  of  some  relation  between 
(i.)  Terms,  or  (ii.)  Propositions,  which  does  not  hold 
between  them.  Or,  taking  the  word  in  a  narrower 
sense,  there  is  Fallacy  whenever  we  conclude  from  one 
or  more  Propositions  to  another,  the  conclusion  not 
being  justified  by  the  premiss  or  premisses.  The  so- 
called  Semi-logical  and  Material  Fallacies  are  reducible 
to  Formal  Fallacies  —  Elemental,  or  Eductive,  or 
Syllogistic,  or  Circular.  Besides  Formal  Fallacies, 
there  are  also    Fallacies  which    can  only   occur  with 

Relative  Propositions, 178-199 

Tables  of  Fallacies, 200-201 


SECTION    XIX. 


PRINCIPLES  AND   CATEGORIES  OF  LOGIC. 

The  foundations  of  Logic  are  the  Principles  which  are  in- 
volved in  making  Assertions  and  in  putting  them  together. 
The  primary  form  of  Proposition  is  the  Categorical; 
hence  we  need  in  the  first  place  a  Principle  of  Categorical 
Assertion.  We  find  such  a  Principle  in  the  Axiom  of 
Identity  in  Diversity,  which  may  be  formulated  thus  :— 
Every  thing  which  can  be  thought  of  or  named  is  an 
Identity  in  Diversity.  This  law  may  be  represented  by 
the  symbolical  statement  AisB\  A  signifying  any  name 
whatever,  and  B  signifying  any  other  name  which  has 


XXll 


CONTEXTS. 


PAGE 


the  same  application  as  A.      The  Law   of  Identity  in 
Diversity  may  not   (any   more   than  the  Principle   of 
Interdependence)  be  generally  admitted  as  prima  facie 
self-evident ;  but  its  acceptance   is    a  necessary   condi- 
tion of  the  acceptance  of  propositions  which  are  at  first 
sight  and  unquestionably  self-evident— e.f/.  Mathematical 
axioms    and    the    Law    of     Contradiction.       And    the 
Principle  of  Interdependence  is  involved  (in  part)  in  the 
Law  of  Identity,  and  in  self-evident  mathematical  axioms. 
And  it  appears  moreover  to  be  involved  in  the  Law  of 
Contradiction,  so  far  at  least  as  the  interdependence  of  the 
presence  of  B  and  the  absence  of  not-B  is  concerned.    And 
so  far,  too,  the  Principle  of  Interdependence  appears 
to   be   directly   self-evident  ;    w^hile,    on   reflection,  the 
Principle  of  Identity  in  Diversity  seems  to  exhibit  this 
same  characteristic  of  self-evidence.     According  to  the 
Law  of  Contradiction   a  proposition  and  its  negative 
cannot  both  be  affirmed— If  A  is  B,   A  is  not  not-B  ; 
and  according  to  the  Law  of  Excluded  Middle  a  pro- 
position   and    its   formal   alternative    cannot    both    be 
denied— Either  A  is  B,   or  A  is  not  B.     These  laws 
are  complementary  to  each  other,  and  are  both  strictly 
self-evident.— The  Law  of  Identity  in  Diversity  may  be 
regarded  ars  the  Principle  of  the  possibility  of  Significant 
Assertion,  the  Law  of  Contradiction  as  the  Principle  of 
Consistency,    and  the   Law  of   Excluded   Middle  as  a 
Principle  of  Completion.     With  these  Principles  must 
be  co-ordinated  that  of  Interdependence  with  its  two 
branches,  the  Law  of  Concomitance  of  characteristics,  and 
the  Law  of  Causation  of  Events.     We  ought  further  to 
include  here  a  statement  which   sums  up  roughly  the 
assumption  on  which  the  Inductive  Methods  are  based, 
namely,  the  rule  that  phenomena  which  are  never  found 
separate  from  each  other  (being  co-existent,  or  succes- 
sive, or  co-variant)  are  Interdependent.     For  Relative 
Inferences,  two  Principles  of  Inter-relation  are  needed— 
(1)  that  all  Relations  are  reciprocal,  (2)  that  any  objects 
that  are  related  indirectly  are   also  related  directly. 
The  corner-stone  of  Logic  is  the   Principle  that  what 
is  Self-evident  ought  to  be  believed.— The  fundamental 
Category  of  Logic  is  Unity  in  Diflference,         .        .         202-211 


CONTENTS. 


XXIU 


Notes — 

I.  Opposition, 

II.  The  Predicables  and  the  Tree  of  Porphyry, 

III.  'Perfect  Induction,' 

IV.  Elliptical  and  Compound  Arguments, 
V.  'The  Deductive  Method,' 

VI.  Mill's  Canons  of  his  '  Four  Methods,' 

Questions, 

Index  and  Logical  Vocabulary, 


PAGE 

213 
214 
218 
219 
222 
224 

226 

263 


ERRATA. 


Page  14,  line  14,  for  {a  x  h)"  rtad  {a  +  h?. 
,,  219,    „    12  from  foot, /or  Syllogisms  read  Propositions. 


PART    I. 


IMPORT  OF  PROPOSITIONS. 


SECTION   I. 

DEFINITION  AND  SCOPE  OF  LOGIC. 

All  knowledge  that  is  communicated  and  recorded 
is  contained  in  Statements  or  Propositions;  and  a 
Statement  or  Proposition  is  an  Assertion  expressed  in 
words.  Now,  we  believe  certain  statements  and  dis- 
believe others,  and,  as  reasonable  creatures,  we  must 
be  prepared  to  give  some  justification,  ahke  for  our 
Belief  and  for  our  Disbelief.  If  we  beheve  any  state- 
ment, we  can  only  justify  our  belief  by  bringing 
forward  other  statements ;  if  we  disbelieve  any  state- 
ment, the  only  method  open  to  us  of  justifying  our 
disbelief  is,  again,  by  bringing  forward  other  statements. 
Any  statement  or  proposition  that  is  called  in  ques- 
tion may  be  shown  to  be  compatible  or  incompatible 
with,  or  an  inference  from,  the  propositions  which  we 
bring  forward.  For  instance,  I  believe  the  statement 
that  hydrocyanic  acid,  in  certain  quantities,  is  a 
swift  and  powerful  poison.    And  if  called  on  to  justify 

A 


ttttMjgiiiiMilifiliiill-ttltftifig 


(   I 


w 


DEFINITION  AND  SCOPE  OF  LOGIC. 


my  belief,  I  might  adduce  the  propositions  (1)  that 
hydrocyanic  acid  has  been  known  to  cause  sudden 
and  violent  death,  (2)  that  Nature  is  uniform. 

Aofain,  I  do  not  believe  the  statement  that  the  Sun 
goes  round  the  Earth.  And  I  justify  my  disbelief  by 
the  considerations  (1)  that  this  hypothesis  does  not 
explain  the  motions  of  the  heavenly  bodies,  and  (2) 
that  no  hypothesis  ought  to  be  accepted  which  does 
not  explain  the  phenomena  to  which  it  is  applied. 

Again,  I  believe  the  statements  that  (1)  Philosophers 
are  fallible,  and  that  (2)  If  equals  be  added  to  equals, 
the  wholes  are  equal — (1)  because  all  men  are  fallible, 
and  philosophers  are  men;  (2)  because  it  is  self- 
evident,  and  what  is  self-evident  ought  to  be  believed 
(cf.  Section  xvi.). 

And  in  every  other  case,  in  order  to  establish,  or  to 
demonstrate  the  falsity  of,  any  propositions  which  are 
questionable  or  questioned,  we  need  to  test  them 
by  considering  their  relation  to  other  propositions. 
Further,  it  is  plain  that,  in  order  either  to  question  or 
to  explain  any  propositions,  we  must  make  use  of 
other  propositions  which  have  some  bearing  upon 
them — that  is,  some  relation  to  them.  The  business 
of  Logic  is  to  show  what  is  the  Import  or  Meaning  of 
Propositions,  and  what  are  the  Relations  between  Pro- 
positions; and  it  is  evident  that  an  inquiry  into  the 
Import  or  Meaning  of  Propositions  is  a  necessary  pre- 
limiinary  to  an  inquiry  into  the  Relations  of  Proposi- 
tions.     Thus,  since  all   Knowledge   is   expressed   in 


DEFINITION  AND  SCOPE  OF  LOGIC.  6 

Propositions,  and  Science  is  systematised  Knowledge, 
it  follows  that  Logic  applies  to  all  Sciences — to 
Psychology  as  well  as  to  the  Natural  Sciences,  to 
Mathematics  as  well  as  to  Grammar,  to  Philosophy 
as  well  as  to  Insurance  and  Statistics.  Hence  Logic, 
as  the  '  Science  of  Propositions,'  is  emphatically  the 
'Science  of  Sciences' — the  Science  of  a  Method 
of  procedure  which  applies  in  every  department  of 
Knowledge. 

If  Logic  is  the  Science  of  Propositions,  it  will 
naturally  start  from  the  standpoint  of  ordinary 
thought,  ascertained  by  reflection  on  such  thought,  as 
expressed  in  ordinary  language.  Tavo  assumptions 
which  appear  to  be  involved  in  ordinary  thought  are, 
that  (1)  the  application  of  terms  is  uniform,  and 
(2)  that  which  is  self-evident  ought  to  be  believed. 
That  is  to  say,  ordinary  thought  assumes  reason  in 
man,  and  trustworthiness  in  language.  The  first 
assumption  may,  in  any  given  case,  turn  out  to  be  un- 
warranted ;  but  in  order  to  prove  that  it  is  so  in  that 
particular  case,  in  order  even  to  doubt  or  to  examine 
that  case,  we  are  bound  to  assume  it  to  some  extent. 
And  what  api^ears  to  be  self-evident  may  sometimes 
turn  out  not  to  be  so ;  but  we  can  only  test  any  given 
case  by  further  appeals  to  what  appears  to  be  self- 
evident.  Hence  it  seems  that,  as  an  indispensable  condi- 
tion of  intelligent  scepticism  in  any  particular  instance, 
we  must  assume — at  least,  provisionally — the  general 
trustworthiness  of  language  and  of  human  intelligence. 


itmiAmiSsii^mMifm 


MiitMm^imii^iii^^M 


SECTION    II. 

ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 

A  Proposition  may  be  defined  as — 
An  assertion  expressed  in  words. 
Propositions  may  be  primarily  divided  into(l)  Cate- 
gorical— e.g.  All  white  violets  are  fragrant,  Honesty  is 
the  best  policy ;  (2)  Conditional — e.g.  If  any  violet  is 
white,  it  is  fragrant ;  (3)  Hypothetical — e.g.  If  ancient 
astronomers  were  right,  the  sun  goes  round  the 
earth ;  (4)  Alternative  or  Disjunctive — e.g.  Any  goose 
is  grey  or  white,  Any  violet  is  fragrant  or  not-white. 
The  sun  goes  round  the  earth,  or  ancient  astronomers 
were  wrong.  (2)  and  (3)  may  be  classed  together  as 
Inferential. 

Proposition 


Categorical 


Inferential 


Alternative 


Conditional 


Hypothetical 


In  investigating  the  import  of  Propositions  we  have 
to  consider  (1)  the  constituent  elements  of  proposi- 
tions, (2)  the  force  of  propositions  as  w^holes.     Any 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS.  5 

Categorical  Proposition  consists  of  Terms  and  Copula. 
For  instance,  in  the  categorical  proposition,  Life  is 
sweet,  Life  and  sweet  are  Terms,  and  is  is  the  Copula. 
And  Life  and  siueet  are  not  only  Terms,  they  are  also 
Names:  as  they  occur  in  the  columns  of  the  dic- 
tionary, for  instance,  they  are  names  merely. 


A  Name  may  be  defined  as — 

A  word  (or  combination  of  words)  applying  to 
some  thing  or  group  of  things,  and  signify- 
ing some  characteristics  of  that  to  which  it 
applies. 
Every  name  is  capable  of  being  used  as  a  term, 
either  alone  or  joined  with  some  modifying  word :  as 
x\ll,  This,  Some,  Most,  Many.  A  name  must  of  course 
apply  to  something  (of  which  it  is  the  name),  other- 
wise it  is  not  the  name  of  anything;  and  it  must 
indicate  some  characteristics  of  that  something,  other- 
wise there  w^ould  be  no  reason  for  applying  it  to 
anything  in  particular.  (The  name  of  anything  is 
inevitably  one  of  the  characteristics  indicated  by  the 
name ;  and  for  us  who  know  the  thing  by  its  name, 
and  must  refer  to  it  by  its  name,  this  characteristic  is 
highly  important.)  This  double  office  of  every  name 
—i.e.  (I)  its  applying  to  something,  and  (2)  its  imply- 
ing some  characteristics  of  that  something — corre- 
sponds to  the  Existence  and  Character  of  the  things 
which  names  refer  to.  In  order  to  be  something,  to 
be  anything  at  all,  a  thing  must  exist  (somehow); 


6  ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 

and  whatever  exists  at  all,  must  exist  somehow,  must 
have  some  characteristics  by  which  it  is  distinguished 
from  other  things.  Take  the  names  (1)  Tree,  (2) 
Ghost,  (3)  Greenness,  (4)  Intangibihty — each  of  them 
is  the  name  of  something  which  has  enough  existence 
to  be  something — (1)  and  (2)  of  things  which  are 
themselves  Subjects  of  Attributes ;  (3)  and  (4)  of 
things  w^hich  are  themselves  Attributes  of  Subjects. 
And  (1)  and  (2)  imply  Characteristics  by  which  Trees 
and  Ghosts  are  distinguished  from  other  Subjects  ot 
Attributes,  from  Ferns,  Solid  Bodies,  etc.;  while  (3) 
and  (4)  imply  Characteristics  by  which  Greenness  and 
Intangibility  are  distinguished  from  other  Attributes 
— from  Whiteness,  Hardness,  Triangularity,  etc. 

We  may  say  that  that  in  the  name  of  anything 
which  corresponds  to  the  Existence  of  the  thing- 
named,  is  the  Application  of  the  name:  and  that 
that  which  corresponds  to  the  Character  of  the  thing 
is  the  Signification  of  the  name.  As  far  as  Applica- 
tion goes,  all  names  are  on  the  same  level — the 
Application  of  a  name  means  simply  that  it  applies  to 
something — that  in  fact  it  is  the  name  of  something. 
But  in  respect  of  Signitication,  names  differ  very 
widely.  E.g.  what  are  called  Proper  Names  differ 
from  all  other  names  in  this,  that  they  imply  no 
distinctive  common  characteristic  in  the  obiects  to 
which  they  apply,  other  than  that  of  being  called  by 
the  name.  (This  distinctive  characteristic  may  be 
highly    important — e.g.   for    purposes    of    reference.) 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS.  7 

Hence— as  the  characteristic  of  having  the  name  can 
be  no  guide  to  the  application  of  the  name  (for,  as 
Jevons  says,  'John  Smith  does  not  bear  his  name 
written    on    his    brow ')— Proper    Names   have   the 
unique  distinction  of  affording  in  themselves   abso- 
lutely no  guidance  to  their  own  application,  in  the 
case  of  any  fresh  object.    When  I  have  seen  and 
known  three  or  four  Lions  or  Triangles,  I  can  apply 
the  name  without  further  information  in  the  case  of 
any  fresh  Lions  or  Triangles  that  I  may  meet  with ; 
but  if  I  have  seen  and  known  three  or  four  John 
Smiths,  that  does  not  help  me  in  the  least  to  recog- 
nise the  next  John  Smith  that  I  meet  with.     Of  all 
the  objects  called  by  the  name  John  Smith  we  can 
only  predicate  (1)  what  is  common  to  all  Subjects,  (2) 
unique  individuality,  (3)  a  distinctive  name,  (4)  what 
the  name  is— that  is  to  say,  John  Smith.  Of  such  names 
as  Lion,  Triangle,  Clumber  Spaniel,  Armadillo,  Four- 
penny-bit,  Triangularity,  Generosity,  Red,  Blue,  Hexa- 
gonal, we  can— without  any  other  knowledge  than  the 
names  afford— predicate  a  number  of  characteristics 
distinctive  of  the  Class   or  Attribute  denominated; 
and  it  is  on  this  account  that  (at  any  rate  when  we 
have  once  learnt  the  application  of  such  names)  we 
are  able  to  recognise  the  objects  to  which  they  apply 
in  fresh  cases.    We  may  of  course  have  a  combination 
.  of  names  of  this  kind  with  Proper  Names— e.r/.  Mad- 
ingley  violets,  London  fogs,  Alexander's  father,  Cesar's 
wife :  and  there  are  certain  individual  names  which 


wafrtJiiftiimariiM 


ifirTiiiMiMMifirfiwB.Mstiimf^...aiitiifrffliiitiii-aiiir«ii:te 


8 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


are    as    fully   significant   as   Class   Names— c.(/.   The 
largest  Continent. 

Between   such   names   as    Fog,   Whiteness,  Violet, 
Fragrant,  and  such  names  as  Sydney,  Maria,  Colney, 
Richmal,    there    come    such    names    as    Saturday, 
December,  Winter,  Czar,  Archbishop  of  Canterbury, 
where  application  is  Hmited  by  some  constant  con- 
dition not  implied  in  the  Signification.     For  instance, 
Winter  means  the  coldest  season  of  the  year,  Satur- 
day means  the  last  day  of  the  week — but  we  could 
not  say  that  it  is  part  of  the  meaning  (or  Signitica- 
tion)  of  Winter  that  in  temperate  zones  it  only  occurs 
at  intervals  of  nine  months,  or  of  Saturday  that  it 
comes  fifty-two  times  in  the  year.     AVhatever  day  has 
the  characteristic  of  being  the  last  day  in  the  week  is 
a  Saturday,  whatever  season  has  the  characteristic  of 
being  the  coldest  season  in  the  year  is  Winter ;  but 
the  appHcation  of  the  names  is  further  restricted  by 
the  circumstance  that  periods  having  these  charac- 
teristics can  only  occur  at  certain  intervals,  and  this 
circumstance   is  not   included   in   the  definitions  of 
Saturday  and  Winter. 

Again  it  would  not  be  included  in  the  Signification 
of  Czar  or  Archbishop  of  Canterbury  that  there  can 
be  only  one  at  a  time,  but  the  application  of  the  titles 
is  limited  by  this  condition. 

We  have  mentioned  that  a  Categorical  Proposition 
may  be  analysed  into  two  Terms  and  the  Copula— e.(/. 
in  Life  is  sweet,  life  and  sweet  are  terms,  and  is  is  the 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


9 


Copula.  Further,  the  two  Terms  are  called  respec- 
tively Subject  and  Predicate.  E.g.  in  the  Proposition 
just  given,  life  is  Subject,  and  sweet  is  Predicate. 
The  Subject  indicates  that  which  is  spoken  about,  the 
Predicate  expresses  what  is  afHrmed  or  denied  about 
that  which  is  indicated  by  the  Subject,  the  Copula  de- 
termines the  relation  between  Subject  and  Predicate. 
If  we  put  *S^  in  the  place  of  life,  and  P  in  the  place  of 
sweet,  we  get  the  form  S  is  P,  which  may  be  taken  as 
a  symbolical  representation  of  any  affirmative  Cate- 
gorical Proposition. 

Term  may  be  defined  as — 

Any  word,  or  combination  of  words,  applying  to 
that  of  which  something  is  asserted  (S),  or  to 
that  which  is  asserted  of  it  (P). 

A  Term  (whether  S  or  P)  may  consist  of  only  one 
word,  as  in  (1)  Snow  is  white,  (2)  Perseverance  is 
admirable;  or  of  several — as  in  (3)  The  Marquis  of 
Salisbury  /is/  the  present  Prime  Minister  of  England, 
(4)  All  men  /are/  liable  to  err.  In  (1)  the  S  applies  to  an 
unorganised  material  substance,  in  (2)  to  an  Attribute, 
in  (3)  to  a  Definite  Individual,  in  (4)  to  a  whole  Class. 
In  (1)  and  (2)  the  P  contains  only  one  word,  in  (3)  it 
contains  six  words,  in  (4)  it  contains  three  words ;  but 
in  all  these  cases  the  office  of  P  is  precisely  the  same 
— namely,  to  give  some  information  about  the  thing 
or  things  indicated  by  S.  What  is  indicated  by  S 
may  be  either  a  Subject  of  Attributes  or  an  Attribute 
of  some  Subject. 


■*"'*"'*^ 


■*^^""^'^'*'*"'"^ai 


10 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


When  a  name  is  used  alone  as  S  or  P  of  a  proposi- 
tion, then  Term-name  and  Temn  coincide — e.g.  in 
Arsenic  is  poison,  Truth  is  strong,  Fritz  is  Emperor, 
Term-name  and  Term  are  in  every  case  coincident. 
In  Some  mistakes  are  irremediable,  we  can  distinguish 
in  the  Subject  of  the  proposition  two  elements — 
that  is,  the  class-name  Mistakes,  and  the  adjective  of 
quantity  Some,  and  these  two  elements  together  make 
up  the  Term  (S).  In  This  man  is  a  genius,  we  may 
regard  S  and  P  as  each  consisting  of  two  elements 
— viz.  class-name  (Man,  Genius)  and  adjective  of 
quantity  (This,  A).  Man,  Genius,  may  be  called  Term- 
names  ;  This,  A,  may  be  called  Term-indicators.  The 
value  of  this  distinction  between  Term  and  Term- 
name  will  be  apparent  when  we  come  to  consider  the 
Import  of  Propositions. 

There  are  certain  important  characteristics  of  names 
which  help  us  to  make  a  broad  and  simple  Classifica- 
tion of  Names,  that  may  precede  and  direct  their  use 
as  terms.  For  while  some  names  may  be  used  as 
terms  (or  term-names)  for  both  S  and  P  of  a  pro- 
position, there  are  other  names  which  can  be  used  as 
P  only.  For  instance,  we  can  say  Trees  are  organised, 
Oaks  are  Trees,  Men  are  fallible,  Negroes  are  Men,  All 
Birds  are  feathered,  All  Thrushes  are  Birds — and  so 
on.  But  we  cannot  say,  e.g.,  Strong  are  steady.  Blue 
is  brittle.  We  should  be  asked,  Strong  ivhat  i  Blue 
what  {  But  if  we  say,  Some  men  are  strong.  The 
Lake  of  Geneva  is  blue,  no  one  feels  it  necessary  to 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


11 


ask.  What  is  strong  ?  or  What  is  blue  i  because  it  is 
clear  that  those  adjectives  refer  to  the  substantives 
that  precede  them.    These  considerations  suggest  that 
the  prominent  element  in  the  names  called  Adjectives 
(names  which  are  adjected  to  others)  is  their  Signi- 
fication  {i.e.   the  characteristics  which  they  imply), 
rather  than   their  Application;    and  this  conclusion 
is  corroborated  by  the  fact  that   in   English,  adjec- 
tives are  not  inflected  when  they  quahfy  plural  sub- 
stantives.    In  German,  also,  adjectives  which  occur 
as  Predicates  of  Propositions  are  not  inflected  to  agree 
with  their  Subjects — e.g.  Der  Himmel  ist  blau.  Das 
Buch  ist  interessant.  Die  Rosen  sind  weiss.     And  we 
may  predicate  adjectives  either  of  Subjects  of  Attri- 
butes, or  of  Attributes — e.g.  A  just  man  is  admirable, 
Perseverance  is  admirable — while  a  name  denoting  a 
Subject   of  Attributes   cannot  be   predicated   of  an 
Attribute,  nor  can  a  name  applying  to  an  Attribute 
be  predicated  of  a  Subject  of  Attributes.     Indeed, 
where  the  S  of  a  proposition  is  an  Attribute  name, 
there  are  very  few  instances  in  which  anything  but 
an  adjective  (or  adjective-phrase)  can  be  predicated. 
If  we  except  such  cases  as  Courage  is  a  Virtue,  Red- 
ness is  a  Colour,  and  cases  in  which  the  Predicate  is  a 
synonym  of  the  Subject — e.g.  Courage  is  Valour — 
we  shall  find  that  most  propositions  which  have  an 
Attribute-name  for  S  have  an  adjective  or  adjective- 
phrase  for  P.     E.g.  Beauty  is  attractive,  Good-temper 
is  delightfid,  Secretiveness  is  repulsive.  Heroism  is 


«mis^iuamt'"^'''^'^''iiUiiiiitim 


12 


ELEMENTS  ()K  CATEGORICAL  PROPOSITIONS. 


imcomiiion.  On  the  other  hand,  propositions  which 
have  Substantive  Names  for  S  may  alwa3's  have  Sub- 
stantive Names  for  P. 

Hence  it  appears  that  we  may  make  a  primary 
division  of  Names  into  Attribute  Names  {e.g.  White- 
ness, Strength),  Adjective  Names  {e.g.  White,  Strong), 
and  Substantive  Names  {e.g.  Man,  Fairy,  Peter, 
Saturday,  Longshanks).  And  in  accordance  with  the 
distinctions  previously  taken  {of.  pp.  6-8)  Substantive 
Names  may  be  divided  into  Common  Names  {e.g.  Bee, 
Oak-tree,  Saucer,  Fairy,  Cause),  Special  Names  (such  as 
Saturday,  Marquis  of  Worcester,  One  o'clock).  Unique 
Names  {e.g.  The  longest  river  in  the  world),  and 
Proper  Names  (such  as  Rose,  Benbow,  Newton,  Swift, 
Patience,  Strong,  Grace,  Longchild).  These  different 
kinds  of  names,  as  above  remarked,  may  be  variously 
compounded. 

Although  many  important  distinctions  in  propo- 
sitions depend  upon  differences  in  their  Terms, 
especially  the  Subject  Terms  {e.g.  any  proposition 
beginning  with  a  class-name  quaHfied  by^^^  or  No,  is 
Universal,  one  beginning  with  a  class-name  quahtied 
by  Some  is  Particular),  yet  the  character  of  Terms  can 
never  be  satisfactorily  settled  until  we  have  considered 
what  their  place  and  special  force  are  in  the  propositions 
to  which  they  belong.  An  isolated  name  can  mostly 
be  classed  on  mere  inspection  as  primarily  adjectival 
or  substantival,  and  so  on;  but  the  terms  of  any 
proposition  must  be  regarded  a.v  parU  of  that  pro- 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


13 


position,  and  only  when  so  regarded  can  they  have 
their  character  definitely  and  fully  determined — this 
character,  of  course,  depending  on  the  character  of 
the  thing  named.  For  instance,  if  I  am  asked  to 
describe  the  name  Whiteness,  I  have  no  hesitation  in 
calling  it  an  Attribute  Name ;  but  if  the  word  White- 
ness is  given  to  me  as  a  term  or  par^  of  a  term,  and  I 
am  required  to  describe  it,  I  can  only  say,  Until  1 
know  the  proposition  in  which  it  occurs,  I  am  unable 
to  do  so.  If,  e.g.,  the  proposition  is,  Whiteness  is  a 
colour,  then  Whiteness  is  an  Attribute  Term;  if  the 
proposition  is.  This  table-cloth  is  whiteness  itself,  then 
I  should  say  that  Whiteness  is  part  of  an  Adjectival 
Term  {ivhiteness  itself  being  equivalent  to  as  white 
as  white  can  he) ;  if  the  proposition  is,  This  whiteness 
is  death-like,  I  should  say  that  Whiteness  is  part  of 
an  Attribute  Term,  This  luhiteness  {this  ivhiteness 
meaning  this  pallor  of  countenance — for  an  exactly 
similar  colour  on  china  or  on  silk,  etc.,  need  not  be 
death -like). 

Terms  may  be  divided  primarily  into  tw^o  classes 
(1)  Uni-terminal,  and  (2)  Bi-terminal  Terms.  (1)  are 
terms  which  can  only  be  used  as  P  of  Categorical 
Propositions;  (2)  are  terms  which  may  be  used  as 
either  S  or  P  of  Categorical  Propositions. 

All  Uni-terminal  Terms  are  Adjectival,  and  the 
only  important  subdivision  of  them  is  into  Relative 
(implying  a  relation  or  dependence  of  objects  con- 
nected in  some  system,  which  may  be  of  any  degree 


14 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


of  complexity,  from  the  simplicity  of  a  class,  or  of  any 
two  related  objects,  to  the  intricacy  of  a  genealogical 
tree)  and  Absolute  (which  do  not  imply  such  relation 
or  dependence).  Any  one  who  has  an  acquaintance 
with  the  '  system '  referred  to  by  a  Relative  Term  can 
draw  from  a  proposition  containing  it  a  greater 
variety  of  inferences  than  is  possible  in  the  case  of 
propositions  which  contain  only  Absolute  Terms 
(compare  E  is  F — Absolute  Proposition — and  E  is 
equal  to  F — Relative  Proposition) ;  hence  the  logical 
importance  of  this  distinction.  Mathematical  Propo- 
sitions o^enerallv  contain  Relative  Terms.     E.a. 

2  +  2  =  4  (2  +  2  /is/  equal  to  4): 

(ax6)--  =  aH2a6  +  6-; 

The  two  sides  RA,  AC  /are  /  equal  to  the  two 
sides  DA,  AC ; 

A  /is/  greater  than  R ; 

6s.  8d.  /is/  one-third  of  £1. 
A  fortiori  argimients  are  simply  a  special  case  of 
arguments  which  turn  upon  Relativity  of  Terms.  All 
kinds  of  terms  are  divisible  into  Relative  and  Absolute. 
Relative  Adject ivals  are  such  as.  Like  R,  Refore  C, 
Equal  to  D,  Less  pinnatifid  than  E,  Out-Heroding 
Herod ;  Absolute  Adjectivals  are  such  as,  Rlue, 
Strong,  etc. 

To  the  division  into  Uni-terminal  and  Ri-terminal 
Terms  there  corresponds  a  division  of  Propositions 
into  what  may  be  called  (1)  Adjectival,  and  (2)  Coin- 
cidental Propositions.    (1)  are  Categorical  Propositions 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


15 


which  have  a  Uni-terminal  Term  for  P,  and  can  neither 
be  converted  nor  (c/.  p.  58)  quantilicated — {e.g.  from 
All  Rushmen  are  short,  I  cannot  proceed  to  say  All 
Rushmen  are  some  short,  nor  Some  short  are  Rush- 
men);  (2)  are  Categorical  Propositions  which  have 
Ri-terminal  Terms  for  both  S  and  P.  As  a  rule  these 
can  be  quantilicated  and  converted.  {E.g.  from  All 
Rushmen  are  savages,  I  can  go  on  to  say,  All  Rush- 
men  are  some  savages,  and  Some  savages  are  Rush- 
men.)  For  obvious  reasons  such  propositions  as, 
Rashness  is  not  courage.  Justice  is  fairness,  Tully  is 
Cicero,  cannot  have  either  S  or  P  quantified.  And 
propositions  of  the  form  Some  R  is  not  Q,  are  not 
considered  to  be  susceptible  of  conversion.  The  dis- 
tinction here  taken  will  be  further  noticed  in  con- 
nection with  Conversion;  and  when  we  come  to 
consider  Syllogism,  it  may  be  seen  that  no  Syllogism 
can  consist  entirely  of  Adjectival  Propositions. 

The  principal  division  of  Ri-terminal  Terms  is  into 
(1)  Attribute  Terms  (having  an  Attribute  Name  for 
Term-name),  and  (2)  Substantive  Terms  (having  a 
Substantive  Name  for  Term-name).  The  Substantive 
Terms  are  Common,  Special,  Unique,  or  Proper,  hav- 
ing respectively  a  Common,  Special,  Unique,  or  Proper 
Name  for  Term-name.  (Term  and  Term-name,  as 
before  observed,  are  sometimes  coincident,  as  in, 
Ryzantium  is  Constantinople.) 

(1)  and  (2),  again,  may  be  divided  into  {a)  Whole 
and  (6)  Partial  Terms  :  e.g.  (1)  and  (2)  (a),  Steadfast- 


iaaM 


^MHSi 


16 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


ness,  Stupidity,  All  men,  The  days  of  the  week, 
Homer;  (1)  and  (2)  (h)  His  courage,  Some  cruelty, 
One  pilgrim,  Several  lapwings,  Two  months  in  the 
year.  One  of  the  Jewish  patriarchs.  Terms  may  also 
be  Definite  (as,  Rembrandt,  All  artists.  This  mathe- 
matician, That  generosity),  or  Indefinite  (as.  Some 
injustice.  Most  poets,  A  robin) :  and  finally  they  may 
be  Relative  (as.  King  of  Greece,  Wife  of  Zeus,  Loaf  of 
bread.  Equality  of  angles.  Congestion  of  the  lungs, 
Death  by  famine,  Day  of  the  week),  or  Absolute  (as. 
Truth,  Fear,  Lion,  April,  Lsaac  Newton). 

It  may  be  noticed  that  many  Technical  and  other 
Terms  which  have  the  form  have  not  the  force  of 
Relative  Terms— e.g.  Fibres  of  Corti,  Will  of  iron, 
Man-of-war. 

I  think  that  the  reason  why  such  names  as  Gold, 
Water,  The  number  six.  The  half-sovereign,  The  word 
and,  The  word  symbol,  and  so  on,  are  always  or 
mostly  used  in  the  singular  number,  is  because 
these  names  apply  to  things  of  which  the  intrinsic 
character  and  value  do  not  vary  from  instance  to 
instance.  Compare  the  corresponding  plural  use  of 
such  names  as  peas,  beans,  etc.  Attribute  Names 
only  take  a  plural  in  a  few  cases — e.g.  colour,  virtue, 
quality,  but  the  application  of  Attribute  Terms  may 
be  Hmited  by  the  term-indicator — e.f/.  Much  cruelty  is 
unthinking. 

The  only  other  constituent  of  a  Categorical  Proposi- 
tion besides  the  Terms,  is  the  Copula.     This  may  be 


ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


17 


Affirmative — is,  are;  or  Negative — is  not,  are  not. 
The  office  of  the  Copula  is  to  express  a  certain 
relation  between  the  Terms.  The  statement  of  this 
relation  involves  a  statement  of  the  Import  of  Propo- 
sitions as  wholes,  and  to  the  consideration  of  this  we 
proceed  in  the  following  Section. 


w 


^m^-yjf.i-...ji«>'i.rMa:-,/ei.i»Aj:i!:  j>ii;a«fl.5j»iCai 


18  ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


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ELEMENTS  OF  CATEGORICAL  PROPOSITIONS. 


19 


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SECTION    III. 

CATEGORICAL  PROPOSITIONS  AS  WHOLES. 

A  Categorical  Proposition  may  be  detined  as — 
A  Proposition  which  asserts  Identity  (or  Other- 
ness) of  Application  in  Diversity  of  Significa- 
tion— (AppHcation  in  Terms,  as  abcady  pointed 
out,   corresponding    to    Existence   in   Things, 
Signification  in  Terms  corresponding  to  Char- 
acter in  Things). 
In  the  Proposition,  Snow  is  white,  the  Application 
of  snoiv  and  white  is  the  same — the  object  which  I 
refer  to,  and  call  snoiv,  is  the  very  same  object  that  I 
refer  to  and  call  white :  ivhite  is  what  the  snow  is — 
the  application  of  P  is  limited  by  the  application  of  S. 
But   the  Signification  of  snow  and  ivhite  is  differ- 
ent— the  two  words  signify  different  characteristics 
or  qualities,  and   would   be  differently  defined.     In, 
Bounce  is  my  brother's  dog.  Bounce  and  niy  brothers 
dog  refer  to  the  same  identical  quadruped,  but  the 
two  words  have  not  the  same  signification.     In,  That 
tree  is  an  oak,   That  tree  and  an  oak  refer  to  one 

20 


categorical  propositions  as  wholes. 


21 


single  identical  object — but  the  signification  of  the 
one  Term  is  diverse  from  that  of  the  other. 
Similarly  in 

The  sky  is  cloudy. 

Patience  is  sometimes  necessary, 

Fanciidlo  is  the  Italian  for  child, 

My  head  is  aching — 
in  each  proposition  the  S  and  the  P  have  an 
identical  reference — they  apply  to  the  very  same 
object;  and  in  each  proposition  the  significations  of 
S  and  P  are  diverse — in  each  case  the  characteristics 
implied  by  P  differ  from  the  characteristics  implied 
by  S. 
Again  in 

All  lions  are  quadrupeds, 
All  lions  and  quadrupeds  refer  to  the  same  objects: 
the  quadrupeds  which  I  assert  that  lions  are,  are 
just  the  quadrupeds  which  are  lions,  and  no  others. 
All  other  quadrupeds — e.g.  tigers,  oxen,  jackals — are 
not  lions.  The  quadrupeds  referred  to  by  the  P  are 
just  as  many  quadrupeds  as  there  are  lions,  and  just 
tlie  very  same  quadrupeds  as  the  lions.  But  all 
lions  and  quad.rupeds  are  differently  defined,  signify 
different  characteristics. 
Or  if  I  say — 

Some  birds'  eggs  are  speckled, 
Soine  birds  eggs  and  specJded,  while  differing  in  signifi- 
cation, refer  to  the  same  objects — the  speclded  which 
I  assert  of  some  birds  eggs  has  no  wider  application 


22 


CATEGORICAL  PIIOPOSITIONS  AS  WHOLES. 


than  just  to  those  very  birds'  eggs  of  which  I  am 
speaking.  To  say  that  it  has,  that  it  refers,  e.g.,  to  all 
speckled  things,  would  be  to  leave  out  of  account  the 
limitation  of  the  application  which  the  term  specldeiL 
has  because  of  its  position  in  the  proposition.  And 
further,  if  all  speckled  things  were  the  Predicate  to 
smne  birds  eggs,  the  Copula  would  have  to  be,  not 
a7'e,  but  are  not. 

Again,  if  in  speaking  of  three  of  Kembrandt's  pic- 
tures— the  '  Night  Watch,'  the  '  Syndics,'  and  the 
*  Portrait  of  his  Mother ' — I  say 

These  pictures  are  some  of  Rembrandt's  master- 
pieces, 
the  objects  referred  to  by  these  pictures  and  by  soTue 
of  Renihrandfs  masterpieces  are  identically  the  same 
— namely,  the  three  which  I  have  just  mentioned  by 
name.  And  of  course,  the  characteristics  signified 
by  the  P  of  this  proposition  are  not  the  same  as  those 
signified  by  the  S. 
In 

5+7=3x4 

( =  Any  5  +  7  /is/  equal  to  any  8  x  4), 
the  application  of  S  (any  5  +  7)  is  identical  with 
the  application  of  P  (equal  to  any  3  x  4).  If  it  Avere 
not  identical,  if  equal  to  any  3x4  had  an  application 
wider  or  narrower,  or  in  any  way  other  than  the 
application  of  any  5  +  7,  then  the  Copula  would  be 
is  not.  For  there  would  be  no  imaginable  ground 
left  for  affirming  P  of  S,  seeing  that  the  two  Terms 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


23 


dilier  in    signification — that  is,    they   could   not   be 
similarly  defined. 
In 

No  rose  is  without  a  thorn 
(=  Any  rose  is-not  without  a  thorn), 
the  Subject  (any  rose)  diliers  in  meaning  from  the 
l^redicate  (without  a  thorn),  and  the  application  of 
the  two  terms  is,  not  identical  but  distinct. 
Again,  in 

Some  flowers  are-not  fragrant, 
Avhile   S   (some   flowers)   and   P   (fragrant)  difler  in 
Signification,   they    also   difler    in   Application — the 
objects  referred   to   by  S   and   by  P  are  altogether 
distinct. 
So,  in 

Courage  is-not  Rashness, 
Collingwood  is-not  my  cousin, 
in  each  proposition,  S  and  P  are  distinct  in  Applica- 
tion and  diverse  in  Signification. 

If  we  take  the  simplest  symboHcal  expression  of 
Categoricals  (afiftrmative  and  negative),  it  is  clear 
that  the  above-given  definition  and  analysis  apply 
to  them.  In  >S'  is  P,  there  is  identity  of  Applica- 
tion, together  with  diversity  of  Signification  between 
S  and  P ;  P  refers  to  the  same  object  or  objects  that 
S  refers  to ;  but  the  character  of  P  is  diverse  from 
the  character  of  S.  In  S  is  not  P,  the  identity 
of  P  with  S  is  denied:  and  their  signification  is 
diverse. 


>aMiaiaaMfi.<!^jyeaj,ggaBaig 


24 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


This  ma}'  be  diagramatically  represented  thus 


SisP(l),  and  >S'  is-  not  P  (2),  represent  every  possible 
Categorical  Proposition.  Therefore  in  any  affirmative 
Proposition,  what  is  P  must  be  regarded  as  identical 
(in  application)  with  whatever  is  S  ;  and  in  negatives, 
whatever  is  P  must  be  regarded  as  distinct  (in  appli- 
cation) from  whatever  is  S.  In  propositions  which 
have  Common  (or  Class)  Names  for  Term-names, 
this  analysis  of  course  holds,  as  well  as  in  all  other 
cases ;  S  and  P  are  in  ever}^  case  identical  or  distinct 
in  Application.  E.g.  in  All  K  is  (^,  All  R  is  Subject, 
and  Q  is  Predicate,  what  is  referred  to  by  All  R 
(whatever  it  is)  is  identical  with  what  is  referred  to 
by  Q  (whatever  that  is).  Otherwise,  of  course,  we 
should  simply  have  to  say.  All  R  is-not  Q.  Similarly 
with  Some  R  is  Q,  Some  R  is  Subject,  and  Q  is  Predi- 
cate, and   Subject   and   Predicate   are   in   each  case 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


25 


identical  though  diverse.  And  in  No  R  is  Q  (=Any 
R  is-not  Q)  and  Some  R  is-not  Q,  Subject  and  Predi- 
cate are  both  distinct  and  diverse. 

The  question  of  the  relation  between  the  classes 
referred  to  by  the  term-names,  in  such  propositions  as 
these,  is  clearly  a  different  question  from  that  con- 
cerning the  relation  between  the  terms  and  that  which 
the  terms  refer  to.  While  the  '  relation '  in  the  latter 
case  can  be  of  two  kinds  only,  the  relations  between 
two  classes  may  be  of  five  kinds. 

For  instance,  if  we  take  R  and  Q  to  symbolise  two 
Class-names,  we  may  have  the  following  relations  of 
Application  between  them : — 

(1)  R  may  completely  coincide  with  Q;  (2)  R  may 
be  included  in  Q ;  (3)  R  may  include  Q  :  (4)  R  and  Q 
may  intersect ;   (5)  R  and  Q  may  exclude  each  other.^ 


1  Cf.  Keynes,  Formal  Logic,  second  edition,  Part  ii.  chap.  vi. 


^HgHUgg 


iiiiTiffiii 


\ 


26 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


Of  the  Class  Propositions  given  above  All  R  is  Q 
may  b^represented  by  (1)  or  (2);  Smne  R  is  Q  may 
be  represented  by  (1),  (2),  (3),  or  (4) :  Some  R  is-not  Q 
may  be  represented  by  (3),  (4),  or  (5) :  No  R  is  Q  is 
represented  by  (5).  These  lour  (lass  Propositions 
are  called  respectively  A  (Universal  Affirmative),  1 
(Particular  Alhrmative),  E  (Universal  Negative),  and 
O  (Particular  Negative).  The  Division  into  Universal 
and  Particular  is  according  to  (Quantity;  that  into 
Affirmative  and  Negative  is  according  to  Quality. 

Further  reference  to  these  considerations  will  be 
necessary  when  we  come  to  consider  Immediate  In- 
ference (Eduction)  as  applied  to  Class  Propositions. 

The  above  account  of  Categorical  Propositions  is 
contirmed  by  a  consideration  of  the  forms  A  is  A, 
A  is  ^aot  A.     While  A  is  A  has  frequently  been  sup- 
posed to  have  a  meaning,  A  is  not  A,  taken  strictly, 
has  always  been  regarded  as  on  a  similar  footing  to 
Aa,  Round-square,  or  any  other  complex  of  contra- 
dictions, for  while   the  Negative  Copula  asserts   the 
distinctvess  or  other-ness  of  the  8  and  P,  their  exact 
similarity  of  signification  involves  identity.    A  is-not 
A    is   therefore  a   form  which   is   self-contradictory. 
(And    similarly   with   A    is    not- A,   only   that    here 
Identity  is  asserted  by  the  Copula  while  Otherness  is 
involved  by  the  Terms.)     But  A  is  A  wants  a  little 
more   examination,  because   it  has   been   so    widely 
regarded   as   having   a   meaning,  and  an   important 
meaning.     We    need   to   ask,   What   thought,  what 


./ 


CATEGORICAL  PROPOSITIONS  AS  WHOLES.  27 

truth,  or  what  assertion  is  it  that  can  correspond  to, 
or  be  expressed  by,  this  form  of  speech  ? 

Let  us  take  a  sentence  of  the  form  A  is  A,  in 
which  A  is  significant— r'.,(/.  Whiteness  is  whiteness, 
or  This  tree  is  this  tree.  In  using  these  forms  of 
words,  how  do  I  go  beyond  what  is  involved  in  the 
mere  enunciation  of  the  words  whiteness,  this  tree  ( 
That  ivhiteness  and  this  tree  should  be  whiteness  and 
this  tree  respectively,  seems  not  a  significant  assertion, 
but  a  presupposition  of  all  significant  assertion— as 
extension  is  a  presupposition  of  colour,  or  ears  of 
sound.  And  if  in  perceiving  whiteness  or  thinking  of 
this  tree  I  ever  need  to  assert  that  whiteness  i^? 
ivhiteness,  or  that  this  tree  is  this  tree,  do  I  not  just 
as  much  need  to  assert  the  same  sentence  separate!)' 
for  both  S  and  P  in  each  case  ?  And  at  what  point 
is  the  process  to  stop  ?  And  if  identity  needs  to  be 
asserted  for  the  Terms,  does  it  not  equally  need  to  be 
asserted  for  the  Cojwia  ?  If  we  need  to  declare  that 
whiteness  is  ivhiteness,  etc.,  do  we  not  also  need  to 
declare  that  Is  is  Is  ?  Unless  we  can  start  by  accept- 
ing Terms  and  Copula  as  having  simply  and  certainly 
a  constant  meaning,  we  can  never  start  at  all.  But 
notwithstanding  all  this,  it  is  still  true  that  sentences 
of  the  form  '  A  is  A '  are  sometimes  used,  and  are 
understood  to  have  a  meaning.  Take,  for  instance, 
such  phrases  as  'Cards  are  Cards'  (Sarah  Battle), 
'  A  man 's  a  man  (for  a'  that),'  '  A  bargain 's  a  bargain.' 
All  these  sayings  are  purely  tautological  and  unmean- 


ggg^^|^w^^ggg;&^^jgatia^w>i'*>^gi 


28 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


ing  in  form,  but  in  using  or  interpreting  them  we 
take  the  S  in  mere  Application,  and  the  P  in  mere 
Signification,  and  thus  put  a  meaning  into  them 
which  is  not  fairly  expressed  by  their  absolute  tauto- 
logy. For  instance,  in  the  last  phrase  what  would  be 
meant  is  probably,  A  bargain  /is/  something  that  must 
be  held  to  and  carried  out, — but  this  is  not  a  state- 
ment that  can  be  properly  symbolised  by  A  /is/  A. 

Both  terms  of  an  affirmative  Categorical  cannot  be 
taken  solely  in  Application,  for  if  so,  every  8  is  F 
must  be  reducible  to  S  is  S,  since  S  and  P  have 
identical  application,  apply  to  the  very  same  objects. 
Neither  can  they  be  both  taken  solely  in  Signification ; 
for,  in  this  case  again,  every  proposition  would  be  of 
the  form  S  is  S — since  any  characteristics,  S,  cannot 
be  asserted  to  be  diverse  characteristics,  P.  And  it 
would  follow  that  the  only  possible  negative  Cate- 
oforicals  would  be  of  the  form  S  is- not  not-S,  which 
is  equally  unmeaning  with  >S'  is  S. 

In  any  Categorical  Proposition,  the  Application  is 
sufficiently  indicated  by  the  S;  identity  or  non- 
identity  of  Application,  as  between  S  and  P,  is  indicated 
by  the  Copula ;  while  diversity  of  Signification  comes 
into  view  only  when  the  P  is  enunciated.  In  regard 
to  any  Categorical  assertion,  we  want  to  know,  in  the 
first  place,  ivhat  it  is  of  which  something  is  affirmed 
or  denied ;  this  knowledge  is  given  with  the  enuncia- 
tion of  the  S,  which  indicates  the  thing  or  things 
spoken  of.     We  want,  in  the  second  place,  to  know 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


29 


ivhat  it  is  that  is  affirmed  or  denied  of  the  thing  or 
things  indicated  by  the  S.  This  information  is  sup- 
plied by  the  P— that  is,  by  its  Signification,  since  it 
IS  evident  that  in  affirmative  propositions  the  Ap- 
plication of  the  P  is  identical  with,  in  negative 
propositions  is  altogether  distinct  from,  that  of  the  S 
(cf.  My  brother's  dog  is  a  mastiff,  My  brother's  dog  is 
not  a  boar-hound).  Hence  it  seems  clear  that  in  the  P 
of  any  proposition,  it  is  naturally  and  inevitably  Signi- 
fication and  not  Application  which  is  prominent. 

To  sum  up  the  results  of  this  Section  so  far :  What 
a  Categorical  Proposition  imports  is  complete  Identity 
or  complete  Distinctness  (Otherness)  of  Apphcation, 
in  Diversity  of  Signification— that  is,  what  the  P 
applies  to  in  affirmative  propositions  is  the  same 
thing  as  Avhat  the  S  applies  to,  but  the  characteristics 
by  which  the  S  refers  to  it  are  diverse  from  the 
characteristics  by  which  the  P  refers  to  it.  The 
affirmative  Copula  imports  identity,  and  identity  can 
only  be  identity  of  Existence  (or  Apphcation).  This 
identity  can  only  be  expressed  or  apprehended  in 
diversity— that  is,  in  difference  of  characteristics.  The 
pencil  with  which  I  am  now  writing  may  be  the 
identical  pencil  with  which  I  wrote  yesterday,  but  it 
can  be  referred  to  as  '  identical '  only  because  it  is 
thought  of  as  having  some  permanence  of  existence. 
Indeed,  that  a  thing  should  have  some  permanence, 
seems  necessary  in  order  for  it  to  be  a  thing  at  all! 
In  negative  Propositions,  what  the  P  applies  to  is  not 


j^-L'Bfc.trfii-'^rttijaafeM 


30 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


what  the  S  appUes  to,  and  what  the  S  signifies  is  not 
what  the  P  signifies. 

CLASSIFICATION  OF  CATEGORICAL  PROPOSITIONS. 

All  Categorical  Propositions  may  be  divided,  in  the 
first  place,  into  Coincidental  and  Adjectival,  the  latter 
havino'  a  Uni-terminal  Term  for  P.  Coincidental  and 
Adjectival  Propositions  have  similar  subdivisions. 
The  principal  of  these  are  (1)  Whole,  (2)  Partial; 
Whole  and  Partial  subdivide,  each,  into  Attribute, 
Proper,  Unique,  Special,  and  Connnon  Propositions 
(ef.  Table).  Whole  Propositions  may  be  singular  or 
plural ;  and,  among  the  latter,  those  which  are  Proper, 
Unique,  or  Special,  may  be  distinguished  as  General 
(e.g.  All  the  Dawson- Wilkinsons  have  arrived,  All  the 
Graces  are  included,  All  the  days  of  the  week  are 
mapped  out):  while  the  plural  Whole  Propositions 
which  have  Common  Names  for  Subject-name  are 
Universal  (e.g.  All  hazel-nuts  are  ripe  in  September, 
All  squirrels  are  playful).  Further  distinctions  and 
subdivisions  are  possible ;  those  of  most  logical  in- 
terest are  Definite  and  Indefinite,  Kelative  and  Ab- 
solute, Distributive  and  Collective.  Those  trees  are 
old,  All  flowers  are  not  in  one  garland,  are  Definite 
Propositions;  Any  shilling  is  worth  twelve  pence, 
Some  ripe  fruits  are  sour,  are  Indefinite;  All  the 
seasons  of  the  year  are  four,  is  Relative ;  A  barking 
dog  seldom  bites,  is  Absolute ;  All  the  seasons  of  the 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


31 


year  are  four,  is  Collective ;  Some  ripe  fruits  are  sour, 
is  Distributive. 

The  Divisions  given  in  the  Table,  and  Definite  and 
Indefinite  Propositions,  receive  their  titles  from  the 
character  of  their  Subject-Term ;  Relative  Propositions 
are  those  of  which  either  Term  is  Relative ;  Absolute, 
those  of  which  both  Terms  are  Absolute.  A  Collec- 
tive Proposition  is  so  called  because  the  P  applies 
only  to  the  S  taken  collectively  (e.g.  All  the  angles  of 
a  triangle  are  equal  to  two  right  angles),  whereas  in  a 
Distributive  Proposition  the  P  may  be  asserted  of 
every  part  or  member  of  the  class  indicated  by  the 
Subject-name  (e.g.  All  the  angles  of  a  triangle  are  less 
than  two  right  angles). 

There  is  finally  the  universally  applicable  distinction 
into  Affirmative  and  Negative  Categoricals,  and  this 
depends  upon  the  affirmative  or  negative  quality  of 
the  Copula. 

■  Differences  in  use  (depending  on  differences  of 
relation  to  other  propositions)  are  connected  with  the 
differences  in  form  of  the  various  kinds  of  Categorical 
I'ropositions  distinguished  above.  These  differences 
will  be  sufficiently  obvious  w^hen  we  come  to  the 
consideration  of  Inferences,  both  Mediate  and  Im- 
mediate. For  instance,  from  Distributive  Universals, 
and  from  them  alone,  both  Distributive  Universals 
and  Particulars  can  be  immediately  inferred.  And  to 
reach  by  Inference  (Mediate  or  Immediate)  an  Uni- 
versal  Proposition,  we   must   always   start   from   an 


32  CATEGORICAL  PROPOSITIONS  AS  WHOLES. 

Universal ;  to  reach  a  General,  we  must  always  start 
from  a  General— and  so  on.  Again,  every  Categorical 
Syllogism  expressing  an  'Inductive'  argument— an 
argument  in  which,  by  help  of  particular  instances, 
we  reach  and  establish  a  new  law— has  an  Universal 
Proposition  for  the  Major  Premiss  and  the  Conclusion. 
When  General  Propositions  and  the  corresponding 
Particulars  are  converted,  the  Predicate  Terms  of  the 
new  propositions  obtained  by  this  conversion  must 
have  indicators  the  same  as,  or  equivalent  to,  those 
which,  they  had  as  Subject  Terms  of  the  old  (con- 
verted) propositions.  For  example,  the  Proposition, 
All  of  my  pupils  have  passed  converts  to  Some  tvho 
have  passed  are  all  my  pupils ;  The  planets  are  bodies 
having  an  ellipticcd  orbit  converts  to  Borne  bodies 
having  an  elliptical  orbit  are  the  planets;  Some  of 
Rembrandt's  pictures  are  master-pieces  converts  to 
Some  master-pieces  are  some  of  Rembrandt's  pictures. 
In  such  cases  as  these,  the  omission  of  the  Term- 
indicator  in  the  new  Predicate  would  entirely  alter 
the  force  of  the  proposition. 


CATEGORICAL  PROPOSITIONS  AS  WHOLES. 


33 


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SECTION    IV. 

RELATIVE  CATEGORICAL  PROPOSITIONS. 

I  MENTIONED  above  (c/.  ante,  p.  14)  the  connection 
between  what  are  called  A  fortiori  Arguments  and 
Relative  Terms — Terms  referring  to  some '  System.'  A 
Proposition  which  has  one  such  Term  for  S  or  P  or 
both,  besides  the  ordinary  Immediate  Inferences 
(Eductions)  which  can  be  drawn  from  it  in  just 
the  same  way  as  from  Absolute  Propositions,  furnishes 
other  immediate  inferences  to  any  one  acquainted 
with  the  system  to  which  it  refers.  These  inferences 
cannot  be  educed  except  by  a  person  knowing 
the    'system';    on    the   other   hand,   no   knowledge 

is  needed  of  the  objects 
referred  to,  except  a  know- 
ledge of  their  place  in  the 
system,  and  this  know- 
ledge is  in  many  cases  co- 
extensive with  ordinary 
intelligence ;  consider,  e.g. 
the  relations  of  magni- 
tude of  objects  in  space, 
of  the  successive  parts  of 
time,  of  familv  connections,  of  number.  From  such 
a  Proposition  as 

C  /is/  the  grandfather  of  D, 

34 


RELATIVE  CATEGORICAL  PROPOSITIONS. 


35 


in  addition  to  such  inferences  as  could  be  drawn  from 
an  Absolute  Proposition  (The  grandfather  of  D  is  C, 
Not  the  grandfather  of  D  is  Not-C,  etc.),  it  is  possible 
for  any  one  having  the  most  elementary  knowledge 
of  family  relationship  to  infer  further  that 
D  /is/  the  grandson 

ofC, 
A  parent  of  D  /is/  a 

child  of  C, 
A  child  of  D  /is/  a 
gi^eat-grandchild  of 
C, 
The  father  of  C  /is/ 
the     great-grand- 
father of  D,  etc. 
From  C  /is/  equal  to  D  ^besides  Something  equal  to 
D  /is/  C,  No  not-equal  to  D  /is/  C,  etc.)  it  can  be 
inferred  that 

D  /is/  equal  to  C, 
C   /is  not/   less 

than  D, 
D /is  not/ greater 

than  C, 
C  /is  not/  greater 

than  D, 
Whatever      is 
greater     than 
C  /is/  greater 
than  D, 
and  so  on  (compare  C  /is/  an  inference  from  D). 


36 


RELATIVE  CATEGORICAL  PROPOSITIONS. 


In  each  of  the  above  examples  we  are  not  dealing 
with  one  object  or  group  in  the  same  way  as  in 
Absohite  Propositions — e.g., 

All  men  /are/  mortal 
Byzantium  /is/  Constantinople 
This  bird  /is/  a  lark— 
we  are  now  considering,  besides  the 
identity  of  application  of  S  and  P,  two 
objects  numerically  distinct,  namely 
C  and  D.      The  S  and  P  of  each 
proposition  have  of  course,  as  just 
observed,  the  same  application ;   but 
an   inspection  of  the   terms  (when 
they  are  understood)  enables  us  to 
know  that  in  each  case  we  are  con- 
cerned with  two  things  (two  Subjects 
of    Attributes,  or    two   Attributes), 
related  in  a  certain  way,  Avhile   of 
the  examples  last  given  this  cannot 
be   said.     In   each  of  the   Relative 
Propositions  given,  what   is  predicated  of  the   S  is 
its  relation    to   another  object,  and   we  are   able    to 
take  that  other  object  and  predicate  of  it  its  relation 
to  the  first  object.     And  where  we  have  two  Relative 
Propositions   as    premisses,    we    may   be    concerned 
with  three  distinct  objects,  and  the  relations  between 
them ;  and  the  point  of  union  may  be  in  one  of  the 
objects,  to  which  both  of  the  others  are  related. 

These   considerations   account   for   the   distinctive 


RELATIVE  CATEGORICAL  PROPOSITIONS.  37 

character  of  Mathematical  and  A  fortiori  etc.,  argu- 
ments. Every  such  argument  can  be  expressed  (at 
greater  or  less  length)  by  help  of  Immediate  In- 
ference (Eduction),  or  by  rigid  Syllogism,  or  by  a  com- 
bination of  both— propositions  being  used  that  state 
expHcitly  principles  or  laws  of  the  systems  referred  to, 
which,  in  the  ordinary  conveniently  abbreviated  form! 
are  only  implied.     E.g.  in 

A  /is/  greater  than  E 
B  /is/  greater  than  C 
A  /is/  greater  than  C, 

(where  we  have  four 
term  -  names),  the 
reasoning  may  be  ex- 
pressed by  a  Condition- 
al Syllogism,  thus  :— 

If  anything  (A)  /is/  greater  than  a  second  thing 

(B),  which  (B)  is  greater  than  a  third  thing  (C) ; 

that  thing  (A)  /is/  greater  than  the  third  (C)  : 
This     thing    (A)    /is/    greater    than    a    second 

thing  (B),  which  (B)  is  greater  than  a  third 

thing  (C) : 

This  thing  (A)  is  greater  than  the  third  thing  (C). 
This  Conditional  may,  of  course,  but  with  increase 
of  awkwardness,  be  reduced  to  the  Categorical  form. 

Among  the  most  important  of  Relative  Propositions 
are  certain  Mathematical  or  Quantitative  Propositions; 
and  with  reference  to  these  the  question  arises,  What 


38 


RELATIVE  CATEGORICAL  PROPOSITIONS. 


is   the   Term-indicator   and   what    the   force  of  the 
Copula  =  in  them  ? 
Take,  e.g., 

(a)  2  +  3  =  6-1 
L— And/r8^  let  2  +  3  and  6  - 1  mean  2  +  3  and  6  - 1 
of  an  assigned  unit  {e.g.  apples,  beads  on  a  wire). 
Then,  taking  =  as  signifying  is  equal  to,  and  2  +  3 
6  —  1  as  signifying  2  units  together  with  3  units,  6 
vunits  minus  1  unit,  may  we  read  (a),  with  the  Subject 
taken  distributively,  as 

Any  (2  +  3)  =  some  (6  - 1 ) 

(i.e.  any  2  +  3  /is/  equal  to   some   6-1  of  the 
assigned  unit)  ? 
We  clearly  could  not  have 

Any  (2 +  3)  =  any  (6-1), 
because  the  objects  denoted  by  the  Predicate  in  that 
case  might  be  the  very  same  objects  denoted  by  the 
Subject,  in  which  case  the  Copula  =  would  be  inappro- 
priate, since  a  thing  cannot  be  said  to  be  eqvMl  to 

itself. 

And  if,  taking  S  and  P  collectively ,i  we  interpret 

(a)  to  mean 

All  (2 +  3)  =  all  (6-1), 
on  this  view  we  might  have 

All  (l)  =  all  (1  +  2  +  3+.. .to  x); 
for  All  I's,  taken  collectively,  embraces  all  units,  how- 
ever grouped. 

1  This  collective  interpretation   is   suggested    by   Mr.    Monck, 
Introduction  to  Logic,  p.  19. 


RELATIVE  CATEGORICAL  PROPOSITIONS. 


39 


Again,  if  we  took  1,  2,  etc.  collectively  to  mean  All 
I's,  All  2's,  etc.,  we  might  have 

1  +  1  =  1  (cf.  Boole's  scheme), 

1  +  1  +  1  =  1, 

1  +  1  =  1  +  2  +  3  +  . ..to  X, 
and  so  on.     But  such  interpretations  would  not  be 
admissible    in    Mathematics,    and    the    appropriate 
copula  here  would  be  is,  not  = . 

If,  however,  we  say  that  2  +  3  =  6  —  1  means 

Any  (2 +  3)  =  some  (6-1) 
there  arises  the  difficulty  that  Simple  Conversion  (as 
commonly  applied  with  the  Copula  =  )  would  give  us 
a  proposition  of  this  form — 

Some  (6-1)  =  any  (2  +  3), 
which  would  not  be  valid  for  the  reason  which  pre- 
vented our  accepting 

Any  (2 +  3)  =  any  (6-1). 
We  might  have 

Some  (2  +  3)  =  some  (6-1), 
or 

These  (2 +  3)  =  those  (6-1),  etc. 
But  here   the  universality  which    we    attribute    to 
Mathematical  Propositions  is  wanting. 

If  we  were  to  interpret  =  as  meaning  is-equal-to-or- 
identical-with  (  =  is-or-is-equal-to),  then  we  could  say 

Any  (2 +  3)  =  any  (6-1), 
and  our  proposition  would  be  universal,  convertible 
and  fitly  expressed. 

If  we  are  dealing  with  assigned  units  of  different 


40 


RELATIVE  CATEGORICAL  PROPOSITIONS. 


valiues  and  having  certain  fixed  ratios  to  each  other, 
then  the  copula  =  is  inevitably  restricted  to  mean  only 
equal  to — 

E.g.    240  pennies  =  £1 — 
for  here  identity  between  the  elements  separated  by 
=  is  impossible ;  what  the  proposition  means  is, 

Any  240  pennies  /is/  [something]  equal  to  any  £1. 


II.— If,  however,  instead  of  referring  to  any  assigned 
units,  we  regard  the  figures  in  question  as  having  the 
most  general  or  abstract  application  possible,  and  take 

2+3=6-1 
to  mean 

The  numbers  2  +  3  =  the  numbers  (3  -  1 , 
the  difficulties  above  referred  to  do  not  arise.     Thus 
understood 


2+8=6-1 


is  equivalent  to 

any  (2  +  3)  ;is  equal  to/  any  (6  —  1) 


RELATIVE  CATEGORICAL  PROPOSITIONS.  41 

(Equal  being  taken  to  mean  exactly  similar  quan^ 
titatively,  while  identical  {nurnero  tantum)  means 
the  very  same  thing.  Thus  a  thing  would  be  equal 
to  some  other  thing,  identical  with  itself). 


SECTION    V. 

INFERENTIAL   PROPOSITIONS. 

Inferential  Propositions  are  of  the  form 

If  A,  C  — 

/  If  E  is  F,  E  is  H 

)  If  E  is  F,  G  is  F 
'•^' jIfEisF,GisH 

V  If  any  E  is  F,  that  E  is  H,  etc. 
If  E  is  F,  If  any  E  is  F,  are  called  Antecedents  (A) ; 
E  is  H,  G  is  F,  G  is  H,  that  E  is  H,  are  Consequents 

(C). 

An  Inferential  Proposition  may  be  defined  as— 
A    Proposition    expressing    a    relation  between 
Antecedent    and  Consequent    such    that    an 
identity  (or  identities)  expressed  or  indicated 
by  the  Consequent  is  an  inference  from  an 
identity  (or  identities)  expressed  or  indicated 
by  the  Antecedent. 
The  class  of  Inferential  Propositions  may  be  divided 
into    two    distinct    species,    called    respectively    (1) 
Hypothetical,  (2)  Conditional    (c/.   Keynes,  Formal 
Logic,  2nd  ed.  pp.  64,  65,  67,  etc.). 


42 


inferential  propositions. 


43 


(1)  differ  from  (2)  in  this,  that  both  A  and  C 
express  (or  indicate)  a  complete  Categorical  Proposi- 
tion.    E.g. — 

If  you  are  right,  he  is  a  good  man. 
If  E  were  F,  E  would  be  H. 

The  A  and  C  of  Hypothetical  are  comparatively 
independent  assertions,  while  the  A  and  C  of  Con- 
ditionals are  comparatively  dependent,  and  incom- 
plete.    Take,  e.g.,  the  Conditional 

If  any  flower  is  scarlet,  it  ( =  that  flower)  is  scentless. 
Any  flower  is  scarlet,  the  A  of  this  proposition,  if 
asserted  in  isolation,  is  equivalent  to  all  flowers  are 
scarlet ;  but  this  is  not  the  meaning  which  it  has  as 
Antecedent.  And  that  flower  is  scentless — the  Con- 
sequent— has  obvious  reference  to  that  which  has 
gone  before,  and  is  obviously  incomplete  in  itself.  (Cf. 
If  any  violet  were  scarlet,  it  would  be  scentless.) 


A  Conditional  Proposition  may  be  defined  as — 
A   Proposition   which  asserts  that  any  member 
of  a  class   indicated  by  a  given  name  and 

particular  way,  may  be 
inferred  to   have   also 
some   further  distinc- 
tion. 
If  any  D  is  E,  that  D  is  F, 

is  the   simplest    unequivocal 

expression  for  a  Conditional,  as  distinguished  from  a 


»Bie««te,imfiiarii^ 


iiHiiiiMriUfi  BitiiWiiiHiB 


44 


INFERENTIAL  PROPOSITIONS. 


Hypothetical.    It  is  a  form  in  which  every  Conditional 
can  be  expressed.     E.g. — 

If  you  pull  the  trigger  of  a  gun  it  will  go  oft' 
reduces  to 

If  any  gun  has  its  trigger  pulled  [by  you],  that 
gun  will  go  off*. 
If  he  told  you  anything,  it  is  true 
reduces  to 

If  anything  was  told  you  by  him,  that  thing  is  true. 

A  Hypothetical  Proposition  may  be  defined  as — 
A  Proposition  in  which  two  (expressed  or  indi- 
cated) Categoricals  (or  combinations  of  Cate- 
goricals)  are  combined  in  such  a  way  as  to 
express    that    one    (the    Consequent)    is    an 
inference  from  the  other  (the  Antecedent). 
It  may  be  observed  that  this  inferential  relation  can 
only  obtain  between  propositions  that  differ  from  each 
other  but  are  not  incompatible. 

The   import   of  an  Inferential   may  be  expressed 
approximately  in  a  Relative  Categorical.     E.g. — 

If  E  is  F,  G  is  H 
is  expressible  as 

G  is  H  /is/  an  inference  from  E  is  F. 
This  proposition  may  be  compared   with   such   a 
proposition  as 

E  /is/  larger  than  F. 
In  both  cases  there  are  two  non- identical  elements 
(G  is  H — E  is  F,  E-F)  having  a  certain  relation  to 


inferential  propositions. 


45 


each  other ;  and  in  both  cases  certain  fresh  proposi- 
tions may  be  inferred  in  addition  to  such  as  are 
inferrible  from  all  categoricals.  The  following  are  ex- 
amples of  equivalent  Inferential  and  Categoricals  :— 

(1)  If  you  are  disappointed,  I  am  sorry. 

(2)  If  all  men   were  perfect,  all  men   would   be 

infallible. 

(3)  If  any  bird  is  a  thrush,  it  is  speckled. 

(1)  =  That  I  am  sorry  is  an  inference  from  your 

being  disappointed. 

(2)  =  That  all  men  are  infallible  is  an  inference  from 

their  being  perfect  (perfect  creatures  being 
infallible). 

(3)  =  That  any  bird  is  speckled  is  an  inference  from 

its  being  a  thrush. 
(3)  May  also  be  naturally  expressed  as  an  Absolute 
Categorical.     E.g. 

Any  bird  that  is  a  thrush  /is/  speckled. 
Hypothetical    Propositions    may    be    divided 
follows : — 

(1)  Formal  or  Self-contained  Hypo- 
theticals — i.e.  those  in  which  the 
Consequent  is  an  inference  from  the 
Antecedent  alone— e.^r.  If  all  R's  are 
Q's,  some  R's  are  Q's.^ 

(2)  Referential  Hypothetical — in 
which  the  Consequent  is  inferred,  not 

^  Hypotheticals  of  this  class  are  self-evident,  and  the  attempt  to 
deny  them  produces  a  self-contradictory  statement. 


as 


46  INFERENTIAL  PROPOSITIONS. 

from  the  Antecedent  alone,  but  from  the  Antecedent 
taken  in  conjunction  with  some  other  unexpressed 

proposition   or   propositions.      They 
may   refer    to   either  (a)   only   one 
unexpressed  proposition,  as  in 
If  M  [these  N]  is  P  [some  Q],  S  is  P 

(•••SisM); 
or  they  may  refer  to  (6)  more  than 
one  unexpressed  proposition,  as  in 

If  that  rope  did  not  break,  the  knot  must  have 
come  undone. 
This  account  of  Hypothetical  Propositions  involves 
the  view  that  the  terms  contained  in  any  Hypo- 
thetical are  all  to  be  identified  in  application,  either 
directly  as  in  (1),  or  indirectly  as  in  (2).  For  instance, 
in  the  example  last  given,  the  whole  reasonmg 
imphed  may  be  as  follows  :— 

That  rope   {A)  was    a    rope    binding   together 
climbers  who  fell  apart  (B). 

A  rope  binding  together  climbers 
who  fell  apart  (B)  must  have 
given  way  (0) ; 
Having  given  way  (C)  it  must 
have  broken  or  the  knot  must 
have  come  undone  (D) ; 
.-.  That  rope  (A)  must  have  broken  or  the  knot 
must  have  come  undone  (D). 

Again,  in 

If  the  work  goes  on,  he  will  not  recover, 
the  reasoning  involved  may  be  as  follows  :— 


INFERENTIAL  PROPOSITIONS. 


47 


If  the  work  goes  on,  great  noise  will  be  made ; 
If  great  noise  is  made  he  will  be  disturbed  by 
it;  If  he  is  disturbed 
he  will  not  be  able 
to  sleep;  Ifhe  is  not 
able  to  sleep  he 
will  die. 
Conditional  Propositions 
may  be  divided  into — 

(1)  Divisional  Condition- 
als, in  which  it  is  asserted  

that  if  any  member  of  a  specified  class  does  not  belong 
to  a  subdivision  indicated  by  the  P-name  of  the  Ante- 
cedent, it  may  be  inferred  to  belong  to  one  indicated  by 
the  P-name  of  the  Consequent.    E.g. 

If  any  Goose  is  not  Grey,  it  is 

White. 
If  any  Peer  is  not  a  Duke,  he 
must  be  a  Marquis  or  an  Earl 
or  a  Viscount  or  a  Baron. 
(These    correspond    to,    and    are 
derivable   from  Divisional   Alterna- 
tives, to   which   also   they   may   be 
reduced.) 

(2)  Quasi-Divisional  Conditionals. 

In   these   the  species  got   by  com-  

bining  the  Term-names  of  the  S  and  P  of  the 
Antecedent  is  referred  to  the  class  indicated  by 
the   P  of  the   Consequent:    but    the   Predicates   of 


Goose. 


Peer. 


liiiiiflraiiiiiaii'iiiiliftlliffiiarrliflirlfift 


48 


INFERENTIAL  PROPOSITIONS. 


(6)  If 


(a) 


Antecedent  and  Consequent  do  not  indicate  (as  in 
Divisional)  a  complete  division  of  the  class  denoted 
by  the  Subject  of  the  Antecedent. 
The  following  are  examples  of  (2)  :— 

(a)  If  any  Violet  is 
White  it  is  Fra- 
grant ; 

any   Fowl    is    a 
Spangled    Ham- 
burgh, it  is  Silver 
or  Golden ; 
(c)  If  any  Fowl  is  a  Plymouth 
Rock  or  a  Spangled  Ham- 
burgh, it  is  a  Handsome 
Bird. 
(We  cannot  tell  from  the  mere  form 
of  a  Conditional  without  reference  to 
the  force  of  the  Terms,  whether  it  is 
Divisional  or  Quasi-Divisional;  but 
when   we   know   the    meaning   and 
application   of    the    terms,   we   can 
deduce   more    inferences    from   the 
Divisional   Propositions   than    from 
the    others.       E.g.    from    the    two 
Divisional  Propositions  given  above, 
we  can  draw  up  complete  Divisions  of 
the  Class  Goose  and  the  Class  Peer). 
The   distinction  between   Hypothetical    and  Con- 
ditional  Inferentials   becomes  very  marked   when  a 


INFERENTIAL  PROPOSITIONS. 


49 


proposition  of  either  kind  is  taken  as  Major  Premiss 
in  a  Syllogism  which  has  a  Categorical  Minor  and 
Conclusion  (c/.  post,  Section  xiv.  and  Table  ix.). 
With  a  Hypothetical  we  get — 
If  A,  C; 
A  (or  not-C) ; 

C  (or  not-A). 
If,  e.g., 
A  =  Honesty  is  not-the  best  policy, 
C=Life  is  not- worth  having, 
our  Syllogism  runs — 

If  Honesty  is  not  the  best  policy,  Life  is  not  worth  having  ; 
Honesty  is  not  the  best  policy  (or  Life  is  worth  having) ; 
Life  is  not  worth  having  (or  Honesty  is  the  best  policy). 

But  taking  a  Conditional  Proposition  as  Major 
Premiss,  we  do  not  for  Minor  simply  affirm  the  A  or 
deny  the  C,  nor  for  Conclusion  simply  affirm  the  C  or 
deny  the  A;  but  we  bring  in  a  fresh  term  as  Subject 
in  Minor  Premiss  and  Conclusion.     E.g. 

If  any  town  has  a  Cathedral,  it  is  a  City; 
The  town  of  Hereford  has  a  Cathedral  ; 
The  town  of  Hereford  is  a  City. 

A  concrete  Syllogism  having  a  Conditional  Major 
and  a  Categorical  Minor  and  Conclusion  is  always 
reducible  (though  the  reduction  may  be  troublesome) 
to  the  form — 

If  any  D  is  E,  that  D  is  F ; 

XD  is  E  (or  XD  is  not  F) ; 

XD  is  F  (or  XD  is  not  E). 


SMiUh-iiiiaiilt^itiiiii 


■aSajaa 


^■••'^-^^^''^■'""iWfjilliiillftlfiillili 


50 


INFERENTIAL  PROPOSITIONS. 


The  real  S  of  the  Antecedent  of  any  Conditional 
is  always  Indefinite  Universal — the  S-name  of  the 
Minor  and  Conclusion  generally  has  either  a  definite 
(particular)  Term-indicator  {e.g.  this,  those),  or  is  dis- 
tinguished from  the  S-name  of  the  Antecedent  by 
some  distinctive  attribute.  We  may  have  a  Syllogism 
of  the  form 

If  any  \)  is  E,  that  \)  is  F ; 
Some  D  is  E ; 
Some  D  is  F — 
but  it  is  unusual. 


INFERENTIAL  PROPOSITIONS. 


51 


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^&q 


SECTION    VI. 

ALTERXxVTIVE  (OR  DISJUNCTIVE)  PROPOSITIONS. 

Alternative    Propositions    are    of   the    following 

forms — 

(1)  S  is  Q  or  T  ; 

Any  Topaz  is  pink  or  yellow — 

(2)  D  isEor  F  isG; 

Relief  must  come  quickly  or  we  must  give  up 

hope — 

(3)  X  or  Y  is  P  ; 

Colin  or  Robin  is  coming— 

(4)  X  is  Q  or  X  is  T— 

(5)  P  is  S  or  S  is  not  P. 

(4)  would  generally  be  expressed  (when  significant 
terms  are  used)  in  the  same  form  as  (2),  but  this 
would  be  in  order  to  avoid  the  awkwardness  of  re- 
iterating in  the  second  alternative  the  Subject  of 
the  first,  instead  of  replacing  it  by  a  pronoun.  E.g. 
instead  of  saying  (a)  The  President  will  be  here  or 
the  President  must  be  ill,  we  should  naturally  say 
(6)  The  President  will  be  here  or  he  must  be  ill; 
but  {a)  and  (6)  have  a   precisely   similar   meaning. 

&2 


alternative  PROPOSITIONS. 


53 


Topaz. 


We  could   not,   however,   express    (2)  in   the   form 
of  (4). 

And  we  could  not  put  (1)  into  the 
form  of  (4).  Any  Topaz  is  pink  or 
any  Topaz  is  yellow,  does  not  con- 
vey the  meaning  of  (1),  which  is, 
Any  Topaz  is  pink  or  [being  not 
pink  is]  yellow.  Alternatives  of  this 
form  correspond  to  Conditionals,  and  in  them  the 
Alternation  does  not  indicate  ignorance  or  indeter- 
minateness,  but  simply  indicates  the  subdivisions  to 
some  one  of  which  any  and  every  member  of  a  given 
class  must  belong.  Also  in  these  Alternatives  we  find 
that  the  reciprocal  dependence  betw^een  the  two  parts 
of  the  proposition  is  even  more  prominent  than  in  the 
corresponding  Inferentials.  There  is  no  important  dif- 
ference between  (3)  and  (2) ;  and  (3)  may  be  expressed 
as,  X  is  P  or  Y  is  P,  without  alteration  of  force;  but 
since  this  expression  is  both  awkward  and  unneces- 
sarily long,  the  elliptical  form  (3)  is  generally  used. 

When  the  X  in  (4)  is  an  Universal  Term,  the 
Alternatives  may  be  called  Subsumptional,  because 
the  Subject  common  to  the  Antecedent  and  the 
Consequent  is  referred  to  the  Predicates  of  Antecedent 
and  Consequent,  as  a  Species  to  Alternative  Genera ; 
e.g.  All  men  are  spiritual  beings  or  mere  animals. 
Alternatives  of  form  (5)  may  be  called  Formal  (c/. 
Keynes,  Formal  Logic,  2nd  edition,  p.  40)  or  Self- 
contained. 


lh^»iiMaa«l&A8B>li^{^itfa>ff  J«iian««&ii>^  «i'<-''*fiSlSiLk^!ltSiSiSSIilHtSSSSIISliSM 


54 


ALTERNATIVE  PROPOSITIONS. 


Any  Alternatives  which  are  not  Formal,  Subsiimp- 
tional,  or  Conditional  may  be  called  Contingent.  E.g. 
The  author  of  these  plays  is  Bacon  or  Shakespeare ; 
A  is  B,  or  C  is  D.  All  Formal,  Subsumptional,  and 
Contingent  Alternatives  reduce  to  Hypotheticals. 

We  may  notice  that  o?*  is  sometimes  used  for  aiul 
in  order  to  avoid  ambiguity — e.g.  All  the  books  in 
red  or  yellow  covers  are  to  be  bound  in  morocco ;  if 
it  were  said  '  in  red  and  yellow,'  the  meaning  would 
not  be  clear.  This  proposition  is  plainly  not  Alterna- 
tive in  meaning,  but  an  elliptical  way  of  expressing  a 
simple  conjunction  of  Categoric als — namely. 

All  the  books  in  red  covers  are  to  be  bound  in  morocco, 
All  the  books  in  yellow  covers  are  to  be  bound  in  morocco. 

Alternatives  must  always  have  some  element  of 
exclusiveness,  otherwise  there  is  no  true  alternation : 
as  far  as  alternatives  are  absolutely  unexclusive,  our 
'  Alternation'  is  of  the  form  A  or  A,  which  means  no 
more  than  A  simply.  Where  the  elements  of  an 
Alternation  are  Propositions,  there  must  be  some 
difference  of  meaning  (however  slight)  in  the  Proposi- 
tions (or  there  is  no  alternation)  and  so  far  there  is 
exclusiveness ;  but  alternatives  may  be  true  together, 
and  so  far  there  is  unexclusiveness.     E.g.  in 

XF  is  a  knave,  or  ZF  is  a  fool, 
there  is  the  indispensable  element  of  exclusiveness; 
i.e.  there  is  difference  of  signification ;  there  is  also  an 
undoubted  possibility  of  unexclusiveness,  in  the  sense 
that  both  predicates  may  be  true  of  XY.     Where  the 


ALTERNATIVE  PROPOSITIONS. 


55 


alternatives  are  Terms,  there  may  be  unexclusiveness 
of  application,  but  there  must  be  some  exclusiveness 
of  signification  or  characteristics.     E.g.  in 

Any  voter  is  a  householder  or  a  ratepayer, 
the  application  of  householders  and  ratei^ayers  is  to 
some  extent  coincident ;  but  in  signification  the  two 
terms  are  exclusive — that  is,  they  would  be  differently 
defined,  the  signification  of  the  one  is  different  from 
that  of  the  other. 

There  is  no  escaping  the  admission  that  in  as  far 
as  any  alternation  cannot  be  reduced  to  a  strictly 
exclusive  form,  the  alternation  vanishes,  just  as  in 
S  is  P,  all  significance  of  assertion  would  vanish  if 
P  turned  out  to  signify  S. 


An  Alternative  Proposition  may  be  defined  as — 
A  Proposition  in  which  a  plurality  of  differing 
elements    (connected    by  or  and  called    the 
Alternatives)  are  so  related   that  not  all  of 
them   can  be  denied,  because  the   denial  of 
some  justifies  the  affirmation  of  the  rest. 
Whately  remarks  {Elements  of  Logic,  p.  67,  9th 
edition)  that  '  A  Hypothetical  Proposition  is  defined 
to  be  two  or  more  Gategoricals  united  by  a  Copula 
(conjunction).'     This  definition,  taken  without  restric- 
tion, would  include  a  vast  number  of  combinations  not 
commonly  called  Hypotheticals;    but   I   mention  it 
here  in  order  to  draw  attention  to  the  fact  that  the 
Categorical  form  of  proposition  is  fundamental — the 


56 


ALTERNATIVE  PROPOSITIONS. 


elements  of  Hypotheticals,  Conditionals,  and  Alterna- 
tives being  Categorical  or  Quasi-categorical.  It  would 
thus  be  possible  to  regard  all  Logic  as  concerned  with 
Categoricals  and  their  combinations — but  this  treat- 
ment would  not  be  in  accordance  with  common  usage, 
or  convenience,  not  to  mention  the  ordinary  practice 
of  logical  text-books. 


ALTERNATIVE  PROPOSITIONS. 


O 


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O 


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57 


SECTION   VII. 

QUANTIFICATIOX   AND  CONVERSION,  AND  THE   MEANING 

OF   SOME. 

Before  passing  on  to  Immediate  Inferences,  it  will 
be  as  well  to  give  a  brief  consideration  to  the  subject 
of  Quantification,  in  ordinary  Class  Propositions  of  the 
A,  E,  I  or  0  form.     Such  propositions  commonly  have 
some  sign  of  quantity  attached  to  the  Subject  and  not 
to  the  Predicate,  and  are  said  to  have  a  quantified 
Subject  and  an  unquantified  Predicate.     It  has  been 
held  by  certain  reformers  in  Logic  that  all  Predicates 
are   naturally  quantified   in   thought,  and   ought   to 
be  explicitly  quantified  in  speech.     This  view  does 
not  seem  to  be  borne  out  by  reflection ;  but  careful 
reflection  does  appear  to  show  that  Quantification  i 
is  an  indispensable  instrument  of  Conversion. 

The  place  of  Quantification  in  Logic  is  very  curious, 
its  function  being  often  as  completely  hidden  from 
those  whose  processes  of  Conversion  involve  it,  as 
the  subterranean  course  of  a  train  in  one   of  the 

1  By  Quantification  (1),  quantijicate  (2),  is  here  meant  (1)  qnanti- 
fying  of  the  Predicate,  (2)  to  qnantify  the  Predicate. 

58 


QUANTIFICATION  AND  CONVERSION. 


59 


loop-tunnels  of  the  Swiss  Alps  would  be  to  an  observer 
who  only  saw  it  rush  into  one  opening,  and  emerge 
again  in  a  few  minutes  from  another,  just  above  or 
just  below.  My  meaning  will  be  best  elucidated  b} 
taking  an  ordinary  proposition  and  tracing  the  changes 
which  it  undergoes  in  Conversion. 
Let  the  proposition  be — 

All  human  beings  are  rational  (1) 
The  ordinary  converse  of  this  is — 


4A11)  Imman 
(beings). 


j^  .  »    (Some)  rational 

borne  rational  creatures  are  \       (creatures). 


human  beings  (2), 


or- 


Some  rational  creatures  are  human  (3). 
(3)  is  perhaps  the  more  perfect  converse,  because  (1) 
and  (3)  resemble  each  other  in  having  an  Adjectival 
Term  for  P,  while  (2)  has  a  Substantive  Term  for  P. 
(1)  and  (3)  are  Adjectival  Propositions,  (2)  a  Coinci- 
dental Proposition.  Adjectival  Propositions  cannot 
be  converted  (cf.  ante,  p.  15).  If  I  alter  the  relative 
position  of  S  and  P  in  (1)  as  it  stands,  and  say- 
Rational  are  all  human  beings, 
it  is  clear  that  Conversion  in  the  logical  sense  has  not 
taken  place ;  for  Rational  is  still  the  Predicate,  and 
all  human  beings  is  still  the  Subject.  The  proposition 
has  been  merely  turned  round.  No  Conversion  of  (1) 
while  it  is  (1),  that  is,  while  it  retains  the  Adjectival 
form,  is  possible.  But  it  may  be  put  into  the  corre- 
sponding Coincidental  form — 

All  human  beings  are  rational  creatures  (4) ; 


60 


QUANTIFICATION  AND  CONVERSION, 


and  with  this  (4)  we  can  deal.    It  is  not,  however,  any 
more  than  the  Adjectival  (1),  directly  convertible.     If 

altered  into — 

Rational  creatures  are  all  human  beings, 
the  proposition   thus   obtained,   besides  being   awk- 
ward, is  ambiguous— it  is  by  no  means  clear  which 
term  is  to  be  taken  as  Subject,  and  the  all  might 
even  be  understood  to  qualify  (or  quantify)  Rational 

creatures. 

The  first  step  towards  real  Conversion  is  taken  when 
we  pass  from  the  unquantificated  Coincidental  (4)  to 
the  quantificated  proposition — 

All  human  beings  are  some  rational  creatures  (5). 
From  this  we  go  on  to  the  quantificated  converse — 

Some  rational  creatures  are  all  human  beings  (6) : 
and  from  (6)  to  the  unquantificated  converse  of  (5)— 

Some  rational  creatures  are  human  beings  (7). 
From  (7)  we  can  pass  to  the  corresponding  Adjectival 

Proposition — 

Some  rational  creatures  are  human  (8). 
It  is  to  be  observed  that  in  going  from  (4)  to  (7),  we 
have  not  only  inserted  a  sign  of  quantity  before  the 
new  Subject-name  (rational  creatures)  which,  as  the 
old  Predicate,  had  not  any  to  start  with  ;  we  have  also 
dropped  the  sign  of  quantity  which  the  new  Predicate 
(human  beings)  had  when  it  was  the  old  Subject- 
name.  Thus,  as  we  began  with  an  unquantificated 
proposition,  so  we  end  with  an  unquantificated  pro- 
position.    The   propositions  which  logicians  (on  the 


AND  THE  MEANING  OF  SOME. 


61 


whole)  have  recognised  and  dealt  with  are  unquanti- 
ficated propositions ;  it  is  for  enabling  us  to  pass  (by 
an  elliptical  procedure)  from  unquantificated  to  un- 
quantificated propositions  that  the  ordinary  rules  of 
Conversion  and  Reduction  of  Class  Propositions  and 
Syllogisms  are  framed ;  it  is  of  unquantificated  pro- 
positions that  the  '  nineteen  valid  moods '  of  the  tra- 
ditional Categorical  Syllogism  are  composed.  It  is 
hardly  necessary  to  remark  that  in  ordinary  speech  it 
is  almost  always  unquantificated  propositions  that  are 
used  when  we  are  dealing  with  Common  names. 

In  converting  an  E  proposition,  we  should  proceed 
as  follows: — Let  the  proposition  to 
be  converted   be,  No    R    is    Q   (1). 
(I) =(2)  Any  R  is  not  Q  (by  gram- 
matical equivalence).    Quantificating 

(2)  we  get,  Any  R  is  not  any  Q  (3). 

(3)  converts  to,  Any  Q  is  not  any  R 
(4).  By  disquantificating  (4)  we 
reach  (5),  Any  Q  is  not  R.  And  (5) 
=No  Q  is  R  (by  grammatical  equiva- 
lence). 

My  view  is  that  the  usage  of  Logic  

and  of  ordinary  speech  is  on  the  whole  to  be  justified,^ 

1  It  is  this  usage  of  both  Logic  and  ordinary  speech,  I  think, 
which  explains  the  common  failure  to  distinguish  between  Terms 
and  Term-names.  Taking,  e.g.,  the  proposition  All  Rs  are  Q\<i  (1), 
our  Terms,  so  far  as  expressed,  are— (a)  All  R's,  (b)  Q's.  Con- 
verting (1)  we  get  (2),  Some  Q's  are  R's,  and  here  our  expressed 
Terms  are  (c)  Some  Q's,  {d)  R's— hence  all  R's  and  R's,  Some  Q's 


62  QUANTIFICATION  AND  CONVERSION, 

and  yet  that  Quantitication  is  possible  and  valid  in  a 
subordinate  office,  as  a  necessary  transformation  stage 
of  propositions.     This  can  be  made  clear  by  refer- 
ence to  the  Import  of  Categorical  Propositions.    What 
a  Categorical  Proposition  affirms  or  denies  is,  it  seems, 
identUy  of  application  of  the  S  and  the  P  in  diver- 
sity of  signification.     Application  of  S  and  of  P  in 
an  affirmative  Categorical  Proposition  are  the  same ; 
signitication  of  the  S  and  P  being,  of  course,  always 
diverse,  unless  we  admit  propositions  of  the  form  A  is 
A,  and  being  in  any  case  diverse  in  all  propositions  of 
the  form  A   is  B.     And  application  is  sufficiently  in- 
dicated by  the  S;  identity  or  otherness  is  indicated 
by  the  Copula :  while  diversity  of  signification  comes 
into  view  only  when  the  Predicate  is  enunciated.     In 
re^nu'd  to  any  assertion,  we  want  to  know  in  the  first 
place  what  it  is  of  which  something  is  affirmed  or 
denied ;  this  knowledge  is  given  with  the  enunciation 
of  the  Subject,  which  indicates  the  thing  or  things 
spoken  of.     We  want,  in  the  second  place,  to  know 
ivhat  it  is  that  is  afHrmed  or  denied  of  the  thing  or 
things  indicated  by  the  Subject.     This  information  is 
supplied  by  the  Predicate— that  is,  by  its  signification 

and  Q's,  are  indiscriminately  called  Termx.  And  a  further  point 
which  throws  light  upon  this,  and  also  upon  the  appropriateness  of 
the  traditional  Canon  and  Rules  of  Categorical  Syllogism  to  Classes 
rather  than  to  Terms,  is  that  we  have  a  practical  interest  in  the 
relations  of  Classes  (which  are  indicated  by  Term-names),  and  we 
are  continually  comparing  propositions  which  have  the  same  Term- 
names,  but  not  the  same  Terms. 


AND  THE  MEANING  OF  SOME. 


63 


—since  it  is  evident  that  in  affirmative  propositions 
the  application  of  the  Predicate  is  identical  with,  in 
negative  propositions  is  altogether  distinct  from,  that 
of  the  Subject.     Hence  it  seems  clear  that  in  the  Pre- 
dicate of  any  proposition,  it  is  naturally  and  inevitably 
signification  and  not  application  which  is  prominent. 
This  is  confirmed  by  the  consideration  that  we  com- 
monly use  Adjectival  rather  than  Coincidental  Propo- 
sitions, if  appropriate  Adjectival  Terms  are  available ; 
and  that  such  terms  in  English  cannot  take  the  sign 
of  the  plural,  though  the  Substantive  Terms  which 
they  qualify  can,  and  though  no  one  doubts  that  the 
application  of  an  Adjectival  Term  is  the  same  as  that 
of  the  Substantive  Term  which  it  qualifies.     It  is  also 
to  be  remembered  that  an  Adjectival  Term  cannot  be 
Subject  in  a  proposition.     Now  if  it  is  the  primary 
function  of  the  S  in  any  Categorical  Proposition  to 
indicate  application,  while  it  is  the  primary  function 
of  the  P  to  indicate  signification,  it  seems  obvious  that 
quantifying  is  appropriate,  and  may  be  necessary,  in 
the  case  of  S,  but  not  in  the  case  of  P,  under  ordinary 
circumstances.     And  a  further  reason  against  admit- 
tmg  Quantification  (except  as  a  transformation-stage) 
in  most  propositions,  is  deducible  from  the  considera- 
tion that  what  propositions  affirm  or  deny  is  the  iden- 
tity of  application  (in  diversity  of  signification)  of  S 
and   P;   for   in   a   quantificated   affirmative,   though 
indeed  identity  of  the  terms  is  still  asserted  (as  it  is 
bound  to  be),  the  fact  that  the  application  of  both 


64 


QUANTIFICATION  AND  CONVERSION, 


terms  is   made  prominent   tends  to  obscure  this— 
especially  where  difference  of  extent  of  the  classes  re- 
ferred to  is  suggested.    It  might  indeed  be  maintained 
that  where  both  terms  of  our  propositions  are  taken 
purely  in  application,  quantificated   propositions   are 
most  appropriate,  being  the  form  of  proposition  which 
makes  the  application  of  both  S   and   P  most  pro- 
minent.    But  both  terms  cannot  be  taken  purely  in 
appUcation.     If,  e.g.,  in   S  is  P,  both  S  and  P  were 
taken  in  r.ppUcation  only,  then  to  say  S  is  P  would 
be  exactly  equivalent  to  saying  S  is  S,  for  the  appli- 
cation of  P  is  the  very  same  as  that  of  S.     But  S  is  S 
is  not  (cf.  ante,  p.  27)  entitled  to  be  called  a  significant 
assertion.     On  the  other  hand,  the  view  here  advo- 
,    cated  of  the  Import  of  Categorical  Propositions  justi- 
fies the  recognition  of  Quantification  as  a   phase  of 
propositions.     For  the  Predicates  of  propositions  have 
application  as  well  as  the  Subjects,^  and  (in  affirmative 
propositions)  an  application  which  is   identical  with 
that  of  the  Subjects.     It  is  therefore  (in  a  Coincidental 
Proposition)  possible,  and  under   certain  conditions 
allowable  and  necessary,  to  make  this  prominent  by 
quantification.     And  the  Subjects  of  propositions  have 
signification :  and  this  may  be  allowed  to  come  into 
prominence  by  dropping  the  sign  of  quantity  (Term- 
Indicator)  which  inevitably  fixes  attention  rather  upon 
the  application  than  the  signification  of  a  term. 

1  Of.  that  in  many  languages  {e.g.  Greek,  Latin,  French)  adjectives 
that  qualify  a  plural  Term  alimyfi  take  the  sign  of  the  plural. 


AND  THE  MEANING  OF  SOME, 


65 


The  above  view  of  Quantification  is  confirmed  and 
illustrated  by  a  consideration  of  the  traditional  logical 
treatment  of  0  Propositions.  Of  the  four  Class  Pro- 
positions, A,  E,  I,  0,  the  first  three  have  always  been 
regarded  as  capable,  the  fourth  as  incapable,  of  Con- 
version. 

We  have  seen  that  propositions  on  their  way  to 
Conversion  have  to  undergo  the  process  of  Quantifi- 
cation. But  the  reason  why  O  (Some  R  is  not  Q)  is 
pronounced  inconvertible  is  not  because  there  is  any 
more  difficulty  in  quantificating  it  than  in  quantificat- 
ing  the  other  propositions,  but  because,  when  the  quan- 
tificated converse  of  0  (Any  Q  is  not  sonie  R)  has  been 
reached,  the  quantification  cannot  be  dropped  without 
an  illegitimate  alteration  of  signification.  For  the 
commonly  accepted  signification  of  the  disquantifi- 
cated  converse  of  0  (Any  Q  is  not  R)  implies  a  quanti- 
fication different  from  that  which  has  been  dropped 
— the  dropped.  P-indicator  being  some,  the  P-indicator 
understood  as  involved  in  the  unquantificated  Proposi- 
tion (Any  Q  is  not  R)  reached  by  dropping  it,  being 
any.  And  as,  at  the  same  time,  ordinary  thought  and 
speech  will  not  admit  the  explicitly  quantificated 
form,  it  is  inevitable  that  a  Logic  which  deals  with 
the  forms  of  ordinary  thought  and  speech  should 
regard  O  as  inconvertible.  To  take  a  concrete 
instance :  the  Proposition,  Some  trees  are  not  oaks 
(1),  becomes  by  quantification  (2)  Some  trees  are 
not  any  oaks.     This  converts  to  (3)  Any  oaks  are  not 

E 


66 


QUANTIFICATION  AND  CONVERSION, 


some  trees.  Dropping  the  quantitication  of  (3),  we 
get  (4)  Any  oaks  are  not  trees,  and  this  would  be 
understood  to  mean  (5)  Any  oaks  are  not  any  trees 
(=No  oaks  are  trees). 

THE  MEANING  OF  SOME. 

If  Quantification  of  ordinary  Categorical  Proposi- 
tions is  recognised  as  admissible  and  necessary  in  the 
process  of  Conversion,  but  a  mere  stage  in  that  process, 
it  seems  desirable  to  inquire  a  little  more  particularly 
into  the  force  and  meaning  of  Propositions  while  in  the 
quantitied  stage.  This  depends  principally  upon  the 
signification  given  to  Some.  Some,  it  is  said,  may 
mean  (1)  'Some  but  not  all';  (2)  'Some  at  least,  it 
may  be  all.'  But  when  the  above  are  offered  as 
interpretations  or  explanations  of  Some,  the  question 
obviously  arises.  What  exactly  does  the  Some  in 
Some  at  least.  Some  at  most,  mean  ?  Must  not  the 
meaning  which  it  has  as  constituent  of  these  expres- 
sions be  its  real  minimum  of  meaning  ? 

Ao-ain,  Some  has  been  defined  to  mean  not  none. 
This  definition  is  more  satisfactory  than  (1)  or  (2), 
since  it  is  wide  enough  to  cover  the  meaning  intended 
by  each  (while  (1)  excludes  (2)  and  is  evidently  not 
applicable  in  all  cases),  and  also  it  does  not  present  a 
direct  and  explicit  circidus  in  definiendo.  But  I  am 
afraid  it  is  still  open  to  the  reproach  of  being  circular ; 
for  how  is  none  to  be  defined  except  as  not  some  i 
And  if  Some  means  merely  not  none,  and  None  means 


AND  THE  MEANING  OF  SOME. 


67 


merely  7iot  some,  what  do  we  know  about  either 
except  that  it  is  the  negative  of  the  other  ?  Som£  is 
not-none  contraposits  [contraverts]  to  None  is  not- 
some,  and  if  we  have  nothing  else  to  say  about  the 
meaning  of  None  and  Some,  we  are  simply  revolving 
in  a  circle  which  is  closed  against  all  connection  with 
other  meanings. 

If  we  ask.  What  is  intended  by,  e.g.,  Some  E,  in 
common  speech  ?  it  must  be  admitted  (and  is  recog- 
nised by  logicians)  that  the  almost  invariable  inten- 
tion  of  the  speaker,   in   any  particular  case,  is   to 
indicate  some  limitation  of  K  making  it  narrower  in 
application   than  All  R  (this  must  be   the  case,  for 
instance,    whenever    it    is   got    by   Sub -alternation 
from  All  R);   or  some  modification  of  R  diverse 
in^  signification  from  mere  R.     Therefore  it  may  be 
said  that  what  is  intended  is  part  (not  all)  of  E,  or 
certain  (somehow  distinguished)  E.     If  All  E  were 
intended,  then  in  order  that  the  intended  meaning 
might  be  unequivocally  conveyed.  All  E  would  be 
used.     Similarly,  if  R  unmodified  were  intended,  R 
unmodified  would  be  used. 

But  it  must  be  admitted  that  Some  E  may  happen 
to  have  the  same  application  as  All  R ;  e.g.  1  may  say. 
Some  scarlet  flowers  are  scentless ;  and  it  may  be  true, 
though  I  did  not  know  it,  that  All  scarlet  flowers  sue 
scentless. 

Or  I  may  say.  Some  (= certain  somehow  distin- 
guished) Cloven-hoofed  animals  are  ruminants;  and 


68  QUANTIFICATION  AND  CONVERSION, 

it  may  turn  out  that  I  might  with  equal  truth 
(whether  or  not  I  was  aware  of  it)  have  asserted 
simply  that  Cloven-hoofed  animals  are  ruminants. 

The  recognition  of  such  cases  as  these,  and  of  other 
cases,  where  one  is  fully  conscious  that  one's  knowledge 
is  indeterminate,  makes  it  clear  that  any  definition  of 
Some  which  restricts  it  to  (1)  Less-than-all,  or  (2) 
Certain-somehow-distinguished  (and  (1)  and  (2)  m- 
volve  each  other),  cannot  be  valid. 

I  propose  to  define  Some  R  as  meaning  An  in- 
definite quantity  or  number  of  R  Such  a  definition, 
it  is  clear,  involves  no  implication  either  (a)  of  there 
being  or  not  being  other  R,  or  (h)  of  what  may  be 
asserted  concerning  those  other  K,  if  there  are  any. 
And  the  definition  will  be  found  to  give  all  the 
meaning  that  is  common  to  Some  in  all  cases,  and 
that  justifies  its  use— that  is,  it  gives  the  whole 
Signification  of  the  word. 

This  account  of  the  meaning  of  Some  makes  the 
question  (which  is  sometimes  asked),  Does  Some 
mean  One  at  least,  or  Two  at  least  ?  appear  irrelevant. 
If  Some  means  merely  an  indefinite  quantity,  quan- 
tifying by  Some  makes  our  Terms  explicitly  indeter- 
minate ;  for  it  excludes  (1)  explicit  universahty,  and 
(2)  definite  limitation.  And  it  affords  no  definite 
determination  of  the  relations  of  any  classes  con- 
cerned. 

The  reason  why  it  can  be  used  where  All  cannot  (as 
in  the  Intraversion  [Conversion  per  Accidens]  of  an 


AND  THE  MEANING  OF  SOME. 


69 


A  proposition),  is  that  it  does  not  explicitly  claim 
Universality.^ 

The  function  of  Quantification  on  the  whole  seems 
to  be  simply  to  bring  into  prominence  the  applica- 
tion-aspect of  the  Predicate. 

The  words  Most,  Few,  All,  Any,  are  explained  as 
follows  by  Dr.  Keynes  (Formal  Logic,  2nd  edition 
pp.  61-64) : — '  Most  is  to  be  interpreted  "  at  least  one 
more  than  half."  Few  has  a  negative  force ;  and  "  Few 
R  are  Q  "  may  be  regarded  as  equivalent  to  "  Most  R 
are  -4K)t  Q "  (with  perhaps  the  further  implication 
"  altha,ugh  <Si077ie  R  are  Q").  ,  .  .  A  few  has  not  the 
same  sigi^ification  as  Few,  but  must  be  regarded  as 
affirmative,  and,  generally,  as  simply  equivalent  to 
Sonie;  e.g.  A  few  R  are  Q=Some  R  are  Q.  .  .  .  All  is 
ambiguous,  so  far  as  it  may  be  used  either  distribu- 
tively  or  collectively.  In  the  proposition,  "All  the 
angles  of  a  triangle  are  less  than  two  right  angles,"  it 
is  used  distributively,  the  predicate  applying  to  each 
and  every  angle  of  a  triangle  taken  separately.  In 
the  proposition,  "All  the  angles  of  a  triangle  are  equal 
to  two  right  angles,"  it  is  used  collectively,  the  pre- 
dicate applying  to  all  the  angles  taken  together,  and 
not  to  each  separately.  .  ,  ,  Any  sls  the  sign  of 
quantity  of  the  subject  of  a  categorical  proposition 


1  The  disastrous  results  of  quantifying  with  Some  when  Some 
means  Not-all,  and  what  is  asserted  of  part  is  denied  of  the  rest,  are 
fully  discussed  in  Dr.  Keynes's  Formal  Logic,  Part  iii.  chap,  ix, 
second  edition. 


fmhim&iiibssimiiMiaiiB^r'--'''^^ 


70 


QUANTIFICATION  AND  CONVERSION, 


(e.g.  any  K  is  Q),  is  logically  equivalent  to  "  all "  in  its 
distributive  sense.     Whatever  is  true  of  any  member 
of  a  class  taken  at  random,  is  necessarily  true  of  the 
whole  of  that  class.     When  not   the  subject  of  a 
categorical  proposition,  Any  may  have  a  different 
signification.     For  example,  in  the  hypothetical  pro- 
position, "If  any  A  is  B,  C  is  D,"  it  has  the  same 
indefinite  character  which  we    logically  ascribe   to 
Scmie ;  since  the  antecedent  condition  is  satisfied  if  a 
single  A  is  B.     The   proposition   might   indeed  be 
written, — If  one  or  more  A  is  B,  C  is  D."  ^ 
'    It  may  be  added  that  although  in  Universal  and 
General  Propositions  the  distributive  All  may  have 
the  same  force  as  Any,  yet  there  are  certain  differences 
— for  Any  may  occur  as  Subject-indicator  in  a  Pro- 
position in  which,  by  signification  of  S  or   P,  the 
application  of  the  Subject  is  restricted  to  one  indi- 
vidual.    E.g.  Any  one  who  wins  this  race  will  have  a 
silver  cup.  Any  person  whom  the  committee  choose 
will  be  appointed  secretary.  Any  one  may  have  my 
ticket  (we  could  not  here  replace  any  by  all).    Any 
is   equivalent   to   the   a  or  an  in  many  proverbial 
sayings;   e.g.   A   woman's   mind    and   winter's    wind 
change  oft.  An  honest  miller  has  a  golden  thumb.  An 
ill  plea  should  be  well  pleaded.     The  force  oi  Any  X 
seems  to  be  this : — A  thing,  and  the  only  condition  of 
acceptance  is  X-ness.     Hence  it  follows  that  Any  may 
be  equivalent  to  All,  and  that  from  the  statement 

*  In  the  above  quotation  I  have  substituted  R  and  Q  for  S  and  P. 


AND  THE  MEANING  OF  SOME. 


71 


Any  X  is  F  we  may  conclude  that  All  X's  are  Y, 
because  X-ness  is  connected  with  Y-ness.  And 
conversely,  from  All  X's  are  Y,  it  follows  that  Any 
X  is  F,  because  from  every  X  being  Y  there  may  be 
inferred  a  connection  between  X-ness  and  Y-ness. 


PART     11. 


RELATIONS    OF   PROPOSITIONS. 


SECTION   VIII. 

GENERAL   REMARKS   ON   THE   RELATIONS   OF 

PROPOSITIONS. 

Propositions  may  be  Compatible  or  Incompatible. 
Compatible  Propositions  are  such  as  may  be  true 
together— e.(/.  M  is  P,  S  is  M ;  Incompatible  Proposi- 
tions are  such  as  cannot  be  true  together — e.g.  M  is  P, 
M  is-not  P. 

Two  Compatible  Propositions  may  be  (a)  one- 
sidedly  or  (6)  reciprocally  inferrible ;  e.g.  (a)  Some  R 
is  Q  is  inferrible  from  All  R  is  Q,  one-sidedly;  (h) 
Some  R  is  Q,  Some  Q  is  R,  are  reciprocally  inferrible 
from  each  other,  (a)  and  (h)  may  be  classed  together 
as  Correlative  Propositions.  Again,  Compatible  Pro- 
positions may  be  connected  with  each  other  not  as 
Inference  and  Inferend,  but  as  complementary  Pre- 
misses—e.^.  All  N  is  R,  All  Q  is  N.  Or  they  may  be 
connected  as  Sub-contraries,  of  which  both  may  be 
true,  but  not  both  can  be  false— e.^.  Some  R  is  Q,  Some 
R  is-not  Q. 


relations  of  propositions. 


78 


Two  (Compatible)  Propositions  taken  together  may 
be  related  to  a  third  (Compatible)  as  Premisses  to 
Conclusion— e.^.  M  is  P  and  S  is  M,  therefore  S  is  P. 
This  Relation  may  be  called  Argumental. 

An  interesting  case  of  relation  of  Propositions  is  the 
relation  between  a  number  of  Propositions  of  the  form 

This  is  R, 
That  is  R, 
That  other  is  R,  etc., 

where  a  precisely  similar  Predicate  is  affirmed  of  a 
number  of  different  Subjects,  each  of  which  refers  to 
a  distinct  object.  It  is  as  the  result  of  a  number  of 
perceptions  that  may  be  represented  by  such  a  set  of 
Propositions,  that  objects  distinct  from  one  another, 
but  similar  in  character,  are  grouped  together  as  a 
kind  of  unity  and  indicated  by  a  Class  Name.  Here, 
as  in  the  case  of  Assertion  and  of  Inference,  there  is  a 
guiding  idea  of  Unity  in  Difference ;  but  in  this  case 
the  Unity  is  a  Unity  between  Attributes  in  different 
objects — i.e.  Similarity  in  Otherness.  A  further  case 
of  relation  is  that  between  any  Whole  Categorical 
Proposition  that  is  Distributive,  and  the  several  Sin- 
gular Propositions  into  which  it  may  be  resolved. 
For  instance.  All  R  is  Q  is  equivalent  to 

Ri  is  Q, 
and  R2  is  Q, 
and    W  is  Q,  etc.,  etc.* 


Of.  Keynes,  Formal  Logic,  2nd  ed.,  n.  2,  p.  58. 


74 


GENERAL  REMARKS  ON  THE 


1 


If  I  can  assert  that  All  R  is  Q,  I  can  assert  that  R\  R^, 
etc.,  are  Q ;  if  I  can  assert  that  R\  R\  etc.,  are  Q,  I 
can  assert  that  All  R  is  Q.     The  Categories  which  we 
use  here  are  those  of  Identity  in  Diversity,  of  Similarity 
in  Otherness,  and  of  the  Unity  of  Parts  and  Whole. 
The  express  inference  is  from   Parts   to  Whole  and 
from  Whole  to  Parts ;  and  the  axiom  of  the  inference 
is  that  what  may  be  said  of  each  member  of  a  Class  or 
Group  may  be  said  of  the  whole  Class  or  Group  distri- 
butively,  and  what  may  be  said  of  a  Class  or  Group 
distributively  may  be  said  of  any  member,  or  group  of 
members,  of  that  Class.    Finally,  from  a  number  of 
Propositions,  such  as 

All  (or  Some,  or  This,  etc.)  R  is  B 

RisC 
RisD 
etc. 
we  can  conclude  that  R-ness  may  co-exist  with  B-ness, 
C-ness,  D-ness,  etc.,  and  that  B-ness,  C-ness,  D-ness, 
etc.,  co-exist  with  Q-ness,  etc.  The  Relations  con- 
sidered in  this  paragraph  may  be  grouped  together 

as  Classific. 

All  other  Compatible  Propositions  (among  Simple 
Categoricals)-e.^.  S  is  P  and  Q  is  R,  etc.— may  be  re- 
garded as  formally  Unattached,  that  is,  they  carry  in 
themselves  no  evidence  whatever  that  either  has  any 
bearing  on  the  other,  no  evidence  that  the  affirmation 
or  denial  of  one  wiU  justify  the  affirmation  or  denial 
of  the  other.     That  is,  there  is  nothing  to  show  that 


7> 


J) 


Jt 


» 


» 


» 


BisQ 
CisQ 
DisQ3 
etc. 


RELATIONS  OF  PROPOSITIONS. 


75 


there  is  IncompatibiHty  or  Subcontrariety  or  Unity 
between  them.  Unity  may  be  a  Unity  of  Identity  in 
Diversity,  of  Similarity  in  Otherness,  or  of  Parts 
and  Whole.  It  is  upon  the  perception  of  the  first- 
mentioned  kind  of  Unity,  namely  Identity  in  Diversity, 
that  all  Assertion  and  all  Inference  are  based,  and 
wherever  we  meet  the  words,  //,  Therefore,  Then, 
Because,  etc.,  indicating  Inference,  or  the  word  Or, 
indicating  Alternation,  it  will  appear  upon  investiga- 
tion (although  the  Propositions  may  not  be  obviously 
and  explicitly  connected)  that  there  is  this  under- 
lying identity.  And  wherever  we  find  the  words.  And, 
But,  Too,  Also,  etc.,  connecting  Propositions  (such 
Propositions  being  both  compatible  and  dissimilar)  the 
prominent  connecting  principle  is  that  of  the  Unity 
of  Parts  and  Whole.  The  Category  of  Parts  and 
Whole  is  the  Category  of  Division,  Classification,  and 
Systematisation  generally.  And  in  all  Asserting, 
Inferring,  Dividing,  Classifying,  and  Systematising 
(and  Classing  also  in  as  far  as  conscious  and  dehberate), 
there  is  some  End  or  Purpose  in  view.  Thus  we  find 
that  Propositions  connected  by  And,  Or,  But,  Therefore, 
and  the  other  conjunctions,  are  understood  not  only 
to  have  some  bearing  upon  each  other,  but  also  to  be 
collocated  for  some  reason.  Propositions  could  not 
reasonably  be  connected  by  conjunctions  unless  they 
really  had  some  relation  to  each  other ;  they  would 
not  be  thus  connected  together  by  any  rational  being, 
unless  there  were  some  purpose  to  be  served  by  doing  so. 


MiMmmmm^^''^'*^-'"^^-^  aiiiiiiiitlliiiria 


76 


GENERAL  REMARKS  ON  THE 


Aiid  signifies  that  the  Propositions  which  it  connects 
are  to  be  taken  together  as  reciprocally  modifying  each 
other,  or  at  least  that  they  have  some  common  refer- 
ence. Where  there  is  no  such  reference  the  conjunc- 
tion is  felt  to  be  inappropriate.  E.g.  it  would  sound 
absurd  and  unmeaning  to  say 

England  is  an  island,  and  Sunday  was  a  fine  day, 

or, 

Mr.  Morley  is  a  Radical,  and  this  is  one  of  Faber's 

pencils. 
But  implies  that  the  Propositions  which  it  connects 
modify  one   another   in   an  unexpected,  adverse,  or 

limiting  sense.     E.g. — 

Jack  will  lend  you  his  gun,  but  you  must  bring 
it  back  to-morrow;  I  shall  be   glad   to    see 
Fanny,   but    I    hope    she  will  not  bring  her 
cousin;  Charlie  has  arrived,  but  he  can  only 
stay  for  ten  minutes. 
In  Or,  If,  Tkerefore,  So,  Became,  etc.,  there  is,  as 
already  observed,  reference  to  an  underlying  identity, 
as,  for  instance,  we  saw  in  the  case  of  //  when  consider- 
ing Inferential  Propositions  (cf.  pp.  46,  47).     Every 
one  feels  that  such  a  combination   of  Categoricals 

as,  e.g. — 

If  Friday  is  the  fifth  day  of  the  week,  April  is  the 

fourth  month  of  the  year ;  If  to-day  is  Sunday, 

there  are  168  hours  in  a  week, 
and  so  on,  are  absurd,  because  there  is  no  inferential 
connection  discoverable  between  the  elements  that  are 


RELATIONS  OF  PROPOSITIONS. 


77 


tacked  together  as  Antecedent  and  Consequent.  The 
mere  introduction  of  a  conjunction  cannot,  of  course, 
confer  relation  upon  essentially  disconnected  elements. 
If  this  could  be  done,  there  would  be  no  reason  why, 
e.g.,  the  insertion  of  the  copula  is  should  not  introduce 
Identity  between  S  and  not-S. 


78 


RELATIONS  OF  PROPOSITIONS. 


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SECTION    IX. 


INFERENCES  IN  GENERAL. 


Any  Proposition  is  an  Inference  from  another  or 
others  when  the  assertion  of  the  former  is  justified  by 
the  latter,  while  the  latter  is,  in  some  respect,  differ- 
ent from  the  former.  E.g.  (1)  P  is  S  is  an  Inference 
from  (2)  S  is  P ;  (3)  S  is  P  is  an  Inference  from  (4) 
M  is  P  and  S  is  M — because  the  assertion  of  (1)  and 
(3)  is  justified  by  (2)  and  (4)  respectively ;  (1)  is  true 
if  (2)  is  true,  and  (3)  is  true  if  (4)  is  true. 

If  an  Inference  is  from  one  Proposition  to  another, 
it  is  an  Immediate  Inference  or  Eduction;  if  an 
Inference  is  from  two  Propositions  taken  together  to 
a  third,  it  is  a  Mediate  Inference  or  Argument. 

Immediate  Inferences  (Eductions)  may  be  either 
from  any  Proposition  to  another  Proposition  of  the 
same  form — that  is,  (1)  from  a  Categorical  to  a  Cate- 
gorical, from  an  Inferential  to  an  Inferential,  or  from 
an  Alternative  to  an  Alternative — e.g.  from  All  R  is 
Q  to  Some  Q  is  R ;  or  (2)  from  any  Proposition  to  a 
Proposition  of  a  different  form — e.g.  from  Any  animal 
that  is  horned  is  a  ruminant,  to  If  any  animal  be 


lgim 


80 


INFERENCES  IN  GENERAL. 


horned  it  is  a  ruminant.  These  two  kinds  of  Educ- 
tion might  conveniently  be  called  (1)  Eversion,  and 
(2)  Transversion,  respectively. 

Mediate  Inferences  (or  Arguments),  whether  Cate- 
gorical, Inferential,  or  Alternative,  may  be  either 
Kelative  or  Absolute.  All  Absolute  Arguments  are 
formal— that  is,  they  are  invariably  cogent,  of  abso- 
lutely general  validity— and  these  Arguments  may 
be  classed  together  under  the  name  of  Syllogism. 
Relative  Arguments— whether  Categorical,  Inferential, 
or  Alternative— are  not  in  a  form  that  is  necessarily 
and  invariably  cogent.  In  an  Absolute  Argument 
there  may  be  Relative  Propositions,  but  the  argu- 
ment does  not  depend  at  all  upon  the  relativity  of 
the  propositions ;  whereas  in  Relative  Arguments,  the 
whole  force  of  the  inference  does  depend  upon  the 
relative  character  of  its  constituent  propositions. 

Relative  Categorical  Arguments  are  very  common 
and  very  important  {cf.  Section  IV.,  and  post,  pp. 
129-132).  Relative  Inferential  and  Alternative  Argu- 
ments— 

E.g.  If  A  is  equal  to  B,  C  is  equal  to  D 
D  is  not  equal  to  C 

.-.  B  is  not  equal  to  A, 

C  is  equal  to  D  or  A  is  not  equal  to  B 
But  D  is  not  equal  to  C 
.*.  B  is  not  equal  to  A 
—are  possible  and  valid,  but  not  commonly  used ;  and 
they  differ  so  little  from  the  corresponding  Absolute 


INFERENCES  IN  GENERAL. 


81 


Arguments,  and  are  so  easily  reduced  to  them,  that 
any  separate  consideration  of  them  seems  super- 
fluous. 

The  term  Deduction  is  frequently  used  as  co- 
extensive with  Mediate  Inference  or  Argument,  but 
it  is  perhaps  even  more  commonly  used  as  applying 
to  all  Mediate  Inferences  except  Inductions ;  and  this 
latter  more  restricted  sense  seems  to  me  the  more 
useful  of  the  two.  For  if  we  are  considering  the 
relation  between  Premisses  and  Conclusion,  the  most 
striking  and  important  difference  of  relation  on  which 
to  found  a  Division  of  Categorical  Mediate  Inferences 
seems  to  be  the  difference  between  Premisses  and 
Conclusion  in  extent  of  application — and  we  see  that 
it  is  upon  this  difference  that  the  current  distinction 
between  'Deduction/  and  ' [Im^erfe^tX induction ' Js . 
based.  For  in  the  latter  the  Conclusion  is  really 
wider  than  one  of  the  Premisses,  while  in  all  other 
Categorical  Mediate  Inferences  the  Conclusion  is 
never  wider  than  either  Premiss,  and  is  frequently 
narrower  than  one  or  than  both. 

Take,  for  instance,  the  following  Arguments : — 

(1)  All  N  is  Q 
All  R  is  N 
All  R  is  Q 

(2)  A  is  equal  to  B 
B  is  equal  to  C 
A  is  equal  to  C 

F 


82 


INFERENCES  IN  GENERAL. 

(3)  A  is  greater  than  B 
B  is  greater  than  C 

A  is  greater  than  C 

(4)  All  N  is  Q 
All  R  is  N 


One     ^ 
Some 
This 
These 
Etc. 


RisN 


(5)  All  N  is  Q 
One    ^ 
Some  >  R  is  N 

Etc.    ) 

One    \ 

Some  V  R  is  Q 
Etc.  3 

(6)  All  N  is  Q 
This  R  is  N 

this  R  is  Q 

(7)  Your  N's  are  Q 
These  R's  are  your  N's 

These  R's  are  Q 

<«)  The-  I  J,,  ,,^  ^ 
(This)  } 
These  )  ^, 

5,  i 


's  are  N 


(This, 

One  (Some,  etc.)  R  is  Q 


INFERENCES  IN  GENERAL.  83 

(9)  That  man  is  Robert  Henderson 
That  man  is  my  eldest  brother 

Robert  Henderson  is  my  eldest  brother 

(10)  Dr.  Lightfoot  is  Lady  Margaret  Professor 
The    Bishop    designate   of  Durham    is    Dr. 

Lightfoot 

The  Bishop   designate  of  Durham   is  Lady 
Margaret  Professor 

(11)  Spring,  Summer,  Autumn,  and  Winter  are 

four  periods  which  are  each  three  months 
long 
Spring,  Summer,  Autumn,  and  Winter  are 
the  four  seasons 

The  four  seasons  are  four  periods,  which  are 
each  three  months  long 

In  all  these  cases,  the  Conclusion  has  no  greater 
extent  of  application  than  either  one  of  the  Premisses. 
In  (1),  (2),  (3),  (7),  (9),  (10),  (11),  both  Premisses  and 
the  Conclusion  have  the  same  extent ;  in  (4)  and  (8), 
both  Premisses  have  a  similar  extent  of  application, 
and  the  Conclusion  in  (4)  is  narrower,  in  (8)  may 
he  narrower;  in  (5),  (6),  one  Premiss  and  the  Con- 
clusion have  similar  extent,  and  the  other  Premiss  is 
wider. 

We  may  illustrate  these  relations  of  extent  by 
simple  diagrams  as  follows ; — 


84 


INFERENCES  IN  GENERAL. 


(a)  Major  Premiss 


Minor  Premiss 


Conclusion 


(b)  Major  Premiss 


Elinor  Premiss 
Conclusion 

(c)  Major  Premiss 
Minor  Premiss 
Conclusion 


(1),  (2),  (3),  (7),  (9),  (10),  (11)  might  be  represented 

by  (a) ;  (4)  by  (h) ;  (8)  by  (a)  or  (h) ;  (5)  and  (6)  by  (c). 

In  an  Inductive  Argument — e.g. 

(12)  Anything  that  has  on  one  occasion  been  cause 

of  Y  /is/  always  cause  of  Y 

An  X  /is/  a  thing  that  has  on  one  occasion 

been  cause  of  Y    

An  X  /is/  always  cause  of  Y 
=  Any  X  is  cause  of  Y 

—the  relation  of  extent  between  the  Premisses  and 
the  real  Conclusion  may  be  represented  diagram- 
matically  thus : — 

(d)    Major  Premiss 
Minor  Premiss 
Conclusion 


Here  the  Major  Premiss  and  Conclusion  are  of  similar 
extent,  while  the  Minor  Premiss  is  narrower  than 


INFERENCES  IN  GENERAL. 


85 


either.  The  Universal  Conclusion  from  one  Universal 
and  one  Particular  Premiss  is  legitimate  because  of 
the  peculiar  form  of  the  Major  Term.  It  may  be 
observed  that  Kelative  Categorical  Arguments  are 
generally  of  the  type  represented  by  the  diagram  (a). 

We  have  already  remarked  that  an  Inference 
differs,  in  some  respect,  from  the  proposition  or  pro- 
positions that  it  is  inferred  from.  S  is  P  i&  not  an 
Inference  from  S  is  P,  but  merely  a  repetition  of  it. 
And  if  we  take  (1)  any  Proposition  (or  Propositions) 
whatever,  and  (2)  any  Inference  therefrom,  the 
meaning  of  (2)  and  the  impression  conveyed  by  it  are 
not  exactly  the  same  as  the  meaning  of  (1)  and  the 
impression  conveyed  thereby.  Even  the  substitution 
of  one  synonym  for  another,  or  the  substitution  of  a 
negative  proposition  for  an  equivalent  affirmative,  is 
not  a  mere  change  of  words,  but  corresponds  to  some 
difference  (however  slight)  in  what  the  words  express. 
There  is,  for  instance,  some  difference  in  sense  between 
All  men  are  mortal,  and  No  men  are  immortal,  though 
these  propositions  are  strictly  equivalent.  A  Mediate 
Inference  appears  to  differ  from  an  Immediate  In- 
ference only  in  being  more  complex. 

This  seems  a  convenient  place  for  inserting  defini- 
tions of  a.  few  terms  which  will  be  frequently  used  in 
succeeding  sections. 

(1)  Equivalent.  Any  two  Categorematic  words 
(or  phrases)  are  equivalent  when  they  have 
identical  Application,  and  any  two  Syncate- 


86 


INFERENCES  IN  GENERAL. 


gorem  tic  words  (or  phrases)  are  equivalent 
when  they  have  the  same  meaning.  E,g, 
London  and  the  Metropolis  of  England  are 
Equivalent  Terms;  also  and  likewise  are 
Equivalent  Syncategorematic  words.  Any 
two  different  Propositions  are  equivalent 
which  are  reciprocally  inferrible — e.g.  S  is  P 
and  P  is  S  are  Equivalent  Propositions. 
Hence  Equivalent  Words  or  Propositions  may  be 
substituted  for  one  another. 

(2)  Inference  (in  narrow  sense),  the  Proposition 

inferred  to. 

(3)  Inferend,  the  Proposition  or  Propositions  in- 

ferred from. 

(4)  Inference  (in  wider  sense),  (2)  and  (3)  taken 

together. 

(5)  To  infer,  to  pass  from  one  or  more  Proposi- 

tions (3),  to  another  Proposition  (2),  (3)  being 
the  justification  for  (2),  and  (2)  and  (3)  being 
in  some  respect  different  from  one  another. 

(6)  Educt,  an  Inference  from  one  Proposition. 

(7)  Educendy  the  one  Proposition  inferred  from. 

(8)  Eduction,  (6)  together  with  (7). 

(9)  Educe,  to  pass  from  (7)  to  (6). 

(10)  Conclusion,  an   Inference  (1)   from   two  (or 

more)  Propositions  taken  together. 

(11)  Premisses,   two    Propositions    from   which    a 

Conclusion  is  drawn. 


INFERENCES. 


87 


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SECTION   X. 

IMMEDIATE   INFERENCES   (EDUCTIONS).^ 

When  we  pass  from  one  Proposition  to  another, 
and  the  latter  is  justified  by  the  former  and  differs 
from  it  in  some  respect,  the  latter  is  an  Immediate 
Inference,  or  Eduction,  from  the  former. 

Eductions  may  have  (I.)  Categoricals  (a),  or  Inferen- 
tial (6),  or  Alternatives  (c),  for  both  Educt  and 
Educend ;  these  Pure  Eductions  may  be  called  Ever- 
sions.  Or  (11.)  they  may  have  a  Categorical  with  an 
Inferential  (a),  or  a  Categorical  with  an  Alternative 
(6),  or  an  Inferential  with  an  Alternative  (c).  These 
Mixed  Eductions  may  be  called  Transversions. 

The  fundamental  kinds  of  formal  Eduction  are 
Conversion,  Obversion,  Subversion  (including  Sub- 
alternation),  and  Extraversion.  All  other  kinds  are 
a  combination  of  some  of  these.  E.g.  Contraversion 
[Contraposition],  Ketro version,  and  Inversion  are  a 
combination  of  Conversion  and  Obversion. 

^  I  have  ventured  in  this  Section  to  suggest  and  use  several  new 
terms  (including  Contraversion  as  a  substitute  for  Contraposition), 
thus — as  I  hope — making  the  whole  terminology  of  Immediate 
Inference  more  complete,  uniform,  and  expressive. 


immediate  inferences  (eductions). 


89 


i. — (a)  categorical  eversions. 
Conversions. 

The  principle  of  Conversion  is,  that  the  Terms  (or 
elements)  of  Propositions  may  be  transposed  (the 
possibility  of  this  as  regards  Categoricals  is  a  direct 
consequence  of  the  identity  of  apphcation  of  S  and 
P).  Thus,  in  Categoricals  the  Subject-Term  of  the 
Convertend  becomes  the  Predicate  of  the  Converse, 
and  the  Predicate-Term  of  the  Convertend  becomes 
the  Subject-Term  of  the  Converse — e.g.  S  is  P  con- 
verts to  P  is  S,  S  is-not  P  converts  to  P  is-not  S. 
Where  the  Subject-Term  is  an  unquantified  Name  or 
Symbol,  there  is  generally  no  doubt  as  to  what  is 
the  proper  converse,  and  no  minor  rules  are  needed, 
in  order  to  guard  against  fallacy. 

E.g.  K  is  Q,  TuUy  is  Cicero,  Courage  is  Valour, 
Marguerite  is  the  French  for  Daisy,  Generosity  is  not 
Justice,  Lord  Hartington  is  not  the  present  Prime 
Minister,  London  is  the  largest  city  in  the  world. 
Genius  is  Patience,  are  converted  by  simple  trans- 
position of  S  and  P. 

But  in  dealing  with  Class  Propositions  that  have 
a  quantified  Subject  and  an  unquantified  Predicate, 
mistake  becomes  more  likely ;  because  in  Conversion 
the  unexpressed  but  implied  Term-Indicator  of  the 
old  Predicate-Name  has  to  be  expressed,  since  that 
Name  is  now  the  Subject-Term;  and  on  the  other 
hand  the  expressed  Term-Indicator  of  the  old  Subject- 


j^ii^^mm^MmmimMtm 


mm 


m 


90 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


Name  becomes  unexpressed  and  merely  implied,  that 
Name  being  the  new  Predicate-Name.  And  a  further 
possible  source  of  mistake  is  this,  that  when  a  Class- 
name  occurs  as  Term  without  an  Indicator,  a  different 
Indicator  is  understood  when  it  is  a  Subject-Term 
from  what  is  understood  when  it  is  a  Predicate-Term. 
For  instance,  in  Trees  are  plants,  Trees  would  be 
understood  to  have  All  as  implied  Term-Indicator; 
in  Oaks  are  Trees,  Trees  would  be  understood  to  have 
Some  as  implied  Term-Indicator.  And  if  we  con- 
verted this  last  Proposition,  it  would  be  to  Some  Trees 
are  Oaks.  If  we  convert  any  A  Proposition — All  R's 
are  Q's — we  pass  to  an  I  Proposition — Some  Q's  are 
R's;  similarly  in  converting  E  and  I  (No  R  is  Q, 
Some  R  is  Q),  we  add  a  Term-Indicator  to  the  new 
Subject-name  (Q)  and  drop  the  previously  expressed 
Indicator  of  the  new  Predicate-name  (R).  As  this 
point  has  already  been  discussed  in  the  section  on 
Quantification,  it  will  be  sufficient  here  to  give  a  table 
of  the  Converses  of  Class  Propositions. 

A.  All  R  is  Q  converts  to      Some  Q  is  R  (I). 
E.  No  R  is  Q  „  No  Q  is  R  (E). 

I.    Some  R  is  Q      „  Some  Q  is  R  (I). 

O.  Some  R  is-not  Q  is  inconvertible.   (0/.  pp.  65,  Q%.) 

{Cf.  diagrammatic  illustration  of  the  possible 
relations  between  any  two  Classes,  p.  25.  For  the 
sake  of  distinction  the  Converse  of  E  and  I  may  be 
called  the  Reverse,  the  Converse  of  A  the  Intra\erse.) 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


91 


Obversions. 

The  principle  of  Obverting  is  that  Any  assertion 
justifies  the  denial  of  its  negative  (cf.  Law  of  Contra- 
diction).    To  take  instances : — 

The  assertion  oi  S  is  F  justifies  me  in  denying  S  is 
not-P — that  is,  from  S  is  P  I  can  proceed  to  S  is-not 
not-P  (the  denial  of  S  is  not  P,  which  is  the  negative 
of  S  is  P) ;  from  Juno  /is-not/  Minerva  I  can  proceed 
to  Juno  /is/  not-Minerva.  From  All  is  fine  that  is  fit, 
I  can  pass  to  Nothing  is  not  fine  that  is  fit.  Here, 
again,  the  only  likelihood  of  difficulty  in  connection 
with  Categoricals  arises  when  we  are  dealing  with 
Class  Propositions ;  but  the  possible  difficulty  in  this 
case  is  extremely  slight,  and  it  is  sufficient  to  give 
the  laws  of  Obverting  Categoricals  and  the  forms  of 
Obversions  in  the  case  of  A,  E,  I,  0. 

A.  All  R  is  Q  obverts  to  No  R  is  not-Q. 


E.  No  R  is  Q  obverts  to  All  R  is  not-Q. 


HiWISiiSMtiaitfitfM^^  riiilflliliiiaiiwiftlilihptiirniiiiiniriniiirff^^ 


92  IMMEDIATE  INFERENCES  (EDUCTIONS). 

I.  Some  R  is  Q  obverts  to  Some  R  is-not  not-Q. 


O.  Some  R  is-not  Q  obverts  to  Some  R  is  not-Q. 


The  laws  for  obverting  Categoricals  are : — 
(1.)  S-name  of  Obvertend  is  S-name  of  Obverse. 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


93 


(2.)  The  negative  of  the  P  of  Obvertend  is  the  P 

of  Obverse. 
(3.)  Obverse  and  Obvertend  differ  in  Quality. 
(4.)    Obverse    and   Obvertend    have    the   same 
Quantity. 
Obversion  will  not  apply  when  =  is  regarded  as  the 
Copula. 

Subversions. 

In  Subverting  Categoricals,  the  passage  is  from  a 
given  Proposition  to  another  which  has  the  same 
Quality  and  a  Subject  of  either  narrower  Application 
or  more  indeterminate  Signification ;  or  a  more  in- 
determinate Predicate.     E.g. 

(1)  All  triangles  are  trilaterals  : 

..  •.  All  isosceles  triangles  are  trilaterals. 

(2)  Some  white  violets  are  fragrant ; 
.  • .  Some  violets  are  fragrant. 

(3)  Topsy  is  an  African  negro ; 
.  • .  Topsy  is  a  negro. 

The  only  kinds  of  Subversion  which  are  of  absolutely 
general  vahdity  ^  are  (2)  and  what  is  called  Subalterna- 
tion — that  is,  Inference  from  a  Whole  Proposition,  an 
A  or  E,  to  a  Particular.    E.g. 

Every  wind  is  ill  to  a  broken  ship, 
subverts  (by  Subalternation)  to 

Some  winds  are  ill  to  a  broken  ship. 
We  may  regard  the  Dictum  de  omni  et  nullo  (cf.  note, 
p.  123)  as  supplying  a  Canon  of  Subalternation. 

^  Cf.  post,  note,  p.  96. 


94 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


ExTR AVERSIONS  (e.g.  Inferences  by  'Complex  Concep- 
tion '  and  by  '  Added  Determinants ')  are  such  as,  A  is 
B,  therefore  AX  is  BX ;  C  is  D,  therefore  C  +  2  is  D  -h  2, 
etc. ;  and  are  a  kind  of  Eduction  with  which  we  are 
all  famihar.  The  principle  of  Extraversion  is,  that  if 
any  qualification  or  determination  (positive  or  nega- 
tive) is  attached  to  a  name  or  symbol,  the  same 
qualification  or  determination  may  be  attached  to 
its  equivalent— but  when  significant  words  are  used 
their  force  becomes  so  variously  and  subtilely  altered 
by  their  context,  that  in  inferences  of  this  kind 
(constant  and  indispensable  as  they  are)  there  is  a 
liabiHty  to  fallacy  which  can  only  be  guarded  against 
by  reference    to   the  special  circumstances  of  each 

case. 

If,  e.g.,  we  inferred  that,  because  a  carpenter  is  a 
man,  therefore  a  good  carpenter  is  a  good  man,  the 
inference  would  be  clearly  unjustifiable :  and  for  this 
reason,  that  the  added  determination  'good'  is  not 
understood  in  the  same  sense  when  it  quaUfies  man 
as  when  it  qualifies  carpenter.  Or  if  we  argue  that 
because  an  acorn  will  grow  into  an  oak,  therefore  an 
acorn  and  a  half  will  grow  into  an  oak  and  a  half,  the 
inference  is  ridiculous,  while  on  the  other  hand  we 
can  infer  that  if  one  acorn  will  grow  into  one  oak,  two 
acorns  will  grow  into  two  oaks.^    Immediate  Infer- 

1  The  Contraverse  (Contrapositive)  of  the  Contraverse  of  any 
Proposition  may  be  regarded  as  an  Extraverse— e.gr.  from  (1)  Lord 
Salisbury  is  the  present  Prime  Minister  of  England,  we  can  infer 
(2)  Not-Lord  Salisbury  is  not-the  present  Prime  Minister  of 
England ;  (2)  being  the  Contraverse  of  the  Contraverse  of  (1),  and 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


95 


ences  of  the  form  Some  XK  is  Q,  therefore  Some  X 
is  Q  and  Some  R  is  Q  (cf.  Hillebrand,  Die  neiien 
Theorien  der  kategorischen  Schlusse,  p.  69)  are,  as 
already  observed,  most  appropriately  classed  with 
Subversions. 

De  Morgan  remarks  somewhere  that  '  All  the  logic 
in  the  world  will  not  enable  me  to  prove  that  because 
a  horse  is  an  animal,  therefore  the  head  of  a  horse  is 
the  head  of  an  animal'  This  is  an  Extraversion 
(Inference  by  Complex  Conception),  and  Logic  can 
prove  it  just  as  much,  or  as  little,  as  it  can  prove  that 
Because  S  is  P,  therefore  P  is  S.  In  each  of  these 
two  cases  it  is  self-evident  that  the  Proposition  in- 
fenced  to  is  true  if  the  Proposition  inferred  from  is 
true.  This  '  proof '  is  of  a  kind  that  we  cannot  go 
beyond,  and  do  not  need  to  go  beyond. 

Extraversion  is  used  to  an  enormous  extent  in 
mathematical  reasoning,  and  here  it  can  always  be 
depended  upon,  because  units  of  quantity  are  not 
intrinsically  altered  by  being  put  together  or  taken 
apart.     Thus,  if 


then 


2  +  5  =  7 

2  +  5-1  =  7-1, 
2+5-1     7-1 


etc.; 


being  also  an  Extraverse.  (It  must  be  remembered,  however,  that 
we  cannot  have  an  unquantiticated  Contraverse  of  an  I  Proposition, 
nor  can  we  obvert  when  any  Copula  except  is  {is  not,  are,  are  not) 
is  admitted.) 


96  IMMEDIATE  INFERENCES  (EDUCTIONS). 

and,  more  generally,  whatever  quantities  or  numbers 
a,  h,  c,  d,  and  x,  stand  for,  if 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


97 


then 


a-\-h     c  +  d 


and  so  on.  Extraversion  may  be  defined  as  a  kind 
of  Eduction  in  which,  from  the  modification  of  one 
of  two  Terms  which  have  identical  application,  we 
infer  a  precisely  similar  modification  of  the  other 
Term.i 

Contrapositions  or  Contraversions. 

In  a  Contraverse  the  old  Subject-name  is  predi- 
cated of  the  negative  of  the  old  Predicate-name,  and 
the  Quality  of  a  Contraverse  differs  from  that  of  the 
Contravertend. 

1  While,  on  the  one  hand,  Extraversion  is  applicable  without 
U.it  in  the  case  of,  e.g.,  Mathen^atical  Propositions,  but  not  .n  th 
case  of  ordinary  Absolute  Propositions  (r/.  ante  PP-^f -^-);^^^^^^ 
other  hand,  Subversion  of  the  form  R  is  Q  .-.  RX  is  Q  which  is 
appl  cable  ;ithout  limit  in  the  case  of  ordinary  Abso^^^^^^^^^^ 
positions,  is  entirely  inapplicable  m  the  case  of  Mathematical 
Propositions.     For  instance,  let 

R  =  2  +  2 
Q  =  4 
X=-l 
then  clearly  RisQ.-.RXisQ 

is  quite  illegitimate.  It  is  obvious  that  any  numerical  modification 
of  \ny  number  R  reduces  it  to  not-R ;  whereas  the  utmost  effect 
of  adding  a  determination,  X,  to  any  non-numerical  class-name,  R, 
is  simply  to  substitute  for  the  genus  R  the  species  XR. 


The  Contraverse  of  any  Categorical  Proposition  is 
obtained  by  first  obverting  that  Proposition,  and  then 
converting  the  obverse.    E.g.  if  is  stiff  contraverts 

to  NOT-STIFF  is-not  IF. 

There  is  no  Contraverse  of  I,  because  its  Obverse 
is  an  0  proposition  (which  cannot  be  converted). 

Retroversions. 

The  corresponding  process  of  first  converting  and 
then  obverting  may  be  called  the  Retroverse.    E.g. 
Some  true  doctrines  are  universally  accepted 

retroverts  to 

Some  things  universally  accepted  are  not  untrue 

doctrines. 

In  a  Retroverse  the  negative  of  the  old  Subject- 
name  is  predicated  of  the  old  Predicate-name,  and  the 
Quahty  of  the  Retroverse  differs  from  that  of  the 
Retrovertend. 

There  is  no  Retroverse  of  0. 

Inversions. 

In  a  Categorical  Inversion  '  we  obtain  from  a  given 
proposition  a  new  proposition,  having  the  contradic- 
tory of  the  original  subject  [name]  for  its  subject 
[name],  and  the  original  predicate  for  its  predicate ' 
(Keynes,  Formal  Logic,  second  edition,  p.  107).  Also 
the  Inverse  of  any  Categorical  Proposition  differs 
from  the  Invertend  in  both  Quantity  and  Quality. 
A  and  E  are  the  only  Categoricals  which  can  be 
inverted.     The  following  are  examples : — 

G 


fij«—aAAiii*iriiiiiii 


AU 


>A^  '*MM*^*iMfcillirrflHMMiMiift^ 


98 


IMMEDIATE  INFERENCES  (EDUCTIONS). 


No  sunshine  is  without  shadow 

inverts  to 

Some  things  that  are  not-sunshine  are  without 

shadow. 
A  friend  in  need  is  a  friend  indeed 

inverts  to 

Some  who  are  not-friends  in  need  are-not  friends 

indeed. 

Only  Coincidental  Categoricals  can  be  converted, 
contraverted,  retroverted,  or  inverted.      Adjectivals 
as  well  as  Coincidentals  may  be  subverted,  obverted, 
and  extraverted. 
Transformations. 

In  addition  to  the  above,  there  is  a  kind  of  Imme- 
diate Inference  that  can  be  drawn  from  Relative 
Propositions  only,  and  may  be  called  Transformation. 
In  Categorical  Transformations  we  pass  from  one 
Proposition  to  another  which  is  an  inference  from  it, 
but  in  which  both  the  Terms  are  new,  owing  to  the 
fact  that  in  the  Inferend,  the  Subject-Term  applies  to 
one  of  two  related  objects,  while  in  the  Inference,  the 
Subject-Term  appUes  to  the  other  of  those  two  objects. 
Such  inferences  can  be  drawn  from  a  Relative  Pro- 
position, without  further  information,  by  any  one  who 
knows  the  System  referred  to  by  the  Proposition. 
E.g.  let  X  and  Y  be  two  soUd  bodies,  bearing  a 
certain  relation  to  one  another  which  may  be 
expressed  in  the  Proposition 
X  /is/  larger  than  Y— 


immediate  inferences  (eductions).  99 

from  this,  if  we  understand  the  relations  of  magni- 
tude in  space,  we  may,  without  any  further  knowledge 
about  X  and  Y,  conclude  that 

Y  /is/  smaller  than  X. 
Again,  from 

IfA  =  B,  C  =  D 

we  can  infer 

IfB  =  A,  D  =  C. 

The  principle  of  Transformations  may  be  stated  as 
follows : — 

If,  of  one  object,  relation  to  a  second  object  is  pre- 
dicated :  then  of  that  second  object  its  implied  relation 
to  the  first  object  may  be  predicated. 

The  above  kinds  of  Eduction  may  be  applied  to 
Inferential  and  Alternative  Propositions.  The  follow- 
ing are  examples : — 

I. — (6)  inferential  eversions. 

Conversions. 

If  A,  C 

If  any  E  is  F,  that  E  is  H 
convert  to 

If  C,  A  may  be 

If  any  E  is  H,  that  E  may  be  F. 

IfXisY,XisZ 

converts  to 

If  X  is  Z,  X  may  be  Y. 


100  IMMEDIATE  INFERENCES  (EDUCTIONS). 

If  any  flower  is  scarlet,  it  is  scentless 

converts  to 

If  any  flower  is  scentless,  it  may  be  scarlet. 

If  life  is  worth  living,  Honesty  is  the  best  policy 

converts  to 

If  Honesty  is  the  best  poUcy,  life  may  be  worth 

hving. 

Obversions. 
IfA,C 
If  any  E  is  F,  that  E  is  H 

obvert  to 

If  A,  not  not-C 

If  any  E  is  F,  that  E  is  not  not-H. 
(0/  Any  EF  is  H,  .-.  (by  Obversion)  Any  EF  is-not 
not-H.) 

If  X  is  Y,  X  is  Z 

obverts  to 

If  X  is  Y,  X  is  not  not-Z. 

If  you  would  know  a  knave,  give  him  a  staff* 

obverts  to 

If  you  would  know  a  knave,  don't  omit  to  give 

him  a  staff". 


Subversions. 


If  A,  C 

If  any  E  is  F,  that  E  is  H 
subvert  to,  e.g., 
If  A,  C  may  be 
If  any  E  is  FK,  that  E  is  H. 


IMMEDIATE  INFERENCES  (EDUCTIONS).  101 


If  X  is  Y,  X  is  ZM 

may  subvert  to 

If  X  is  Y,  X  is  Z. 
If  Charles  i.  had  not  deserted 
Strafford,  he  would  be  more 
deserving  of  sympathy 
may  subvert  to 

If  Charles  i.  had  not  deserted  Strafford,  he  might 

be  more  deserving  of  sympathy. 
If  any  violet  were  scarlet,  that  violet  would  be 
scentless 
subverts  to,  e.g., 

If  any  violet  were  bright  scarlet,  that  violet  would 
be  scentless. 

EXTRAVERSIONS. 

If  A  is  greater  than  B,  then  B  is  less  than  A 
extraverts  to,  e.g., 

If  A  is  three  times  greater  than  B,  then  B  is 
three  times  less  than  A. 

If  X  is  Y,  X  is  Z 
extraverts  to,  e.g., 

If  X  is  QY,  X  is  QZ. 

CONTRAVERSIONS. 

If  A,  C 

IfEisF,  EisH 
contravert  to 

If  not  C,  not  A 

If  E  is  not  H,  E  is  not  F. 


102  IMMEDIATE  INFERENCES  (EDUCTIONS). 

If  money  goes  before,  all  ways  lie  open 

contraverts  to 

If  some  ways  are  not  lying  open,  money  does  not 
go  before. 

Retroversions. 

If  A,  C 
IfEisF,  EisH, 

retrovert  to 

If  C,  not  not-A  may  be 

If  E  is  H,  E  may  be  not  not-F. 

If  he  is  quiet,  he  is  in  mischief 
retroverts  to 

If  he  is  in  mischief,  he  may  be  not  making  a 
noise. 

Inversions. 

If  A,  C 

If  E  is  F,  E  is  H 

invert  to 
* 
If  not  A,  C  may  be  not 

If  E  be  not  F,  E  may  be  not  H. 

If  all  men  are  liable  to  mistakes,  all  men  should 
be  modest 
inverts  to 

If  some  men  are  not  liable  to  mistakes,  some 
men  need  not  be  modest. 


immediate  inferences  (eductions).        103 

Transformations. 

If  A  is  equal  to  B,  C  is  equal  to  D 
transforms  to,  e.g., 

If  B  is  equal  to  A,  D  is  equal  to  C. 

I. — (c)  ALTERNATIVE  EVERSIONS. 


Conversions. 

Either  C  or  not-A 
Either  E  is  H  or  E  is 
not  F 

convert  to 

A  may  be,  or  C  is  not 
Either  E  may  be  F  or 
E  is  not  H. 

Obversions. 

Either  C  or  not  A 
Either  E  is  H  or  E  is 
not  F, 
obvert  to 

Either    not    not-C    or 

not  A 
Either  E  is  not  not-H 
or  E  is  not  F. 


Either  Honesty  is  the 
best  policy,  or  Life  is 
not  worth  living. 

Either  Life  may  be 
worth  living  or  Hon- 
esty is  not  the  best 
policy. 

(Either  the  roads  are 
wet  or  rain  has  not 
fallen. 


Either  the  roads  are 
not  dry  or  rain  has 
not  fallen. 


asMitiaiiiiiiMiiiiiHa 


104  IMMEDIATE  INFERENCES  (EDUCTIONS). 

Subversions. 

Either  C  or  not  A,  f  Either    a    violet    is    a 

Either  E  is  KH  or  E  is  |      scentless   abnormity, 
not  F,  \     or  it  is  not  scarlet, 

may  subvert  to 

Either  C  may  be  or  A 

is  not 
Either  E  is  H  or  E  is 
not  F. 


Either  a  violet  is  an 
abnormity,  or  it  is 
not  scarlet. 


EXTRAVERSIONS. 

Either  E  is  H  or  E  is 
not  F, 

extravert  to,  e.g., 


Either  a  speaker  must 
be  convinced  or  he  is 
not  convincing, 


Either  DE  is  H  or  DE  i 
is  not  F. 


Either  a  speaker  must  be 
intensely  convinced, 
or  that  speaker  is  not 
intensely  convincing. 


CONTRAVERSIONS. 

Either  C  or  not  A 
Either  E  is  H  or  E  is 
notF, 


Either  the  streets  are 
wet,  or  rain  has  not 
fallen, 


IMMEDIATE  INFERENCES  (EDUCTIONS).  105 


contravert  to 

Either  not  A  or  C ;  ( Either    rain    has    not 

Either  E  is  not  F,  or  e\      fallen,  or  the  streets 
is  H  (or  not  not-H).     I     are  not  dry. 

Retroversions. 

Either  E  is  H  or  E  is 

notF, 


r  Either  the  streets  are 
wet,  or  rain  has  not 
fallen, 


retrovert  to 

Either  E  may  be  not  T  Either  the  streets  are 

not-F    or   E  is    not  \      dry  or  rain  may  have 
H.  I     fallen. 

Inversions.  r^-^^^^  ^.^^^^^  ^^^  f^^_ 

Either  E  is  H  or  E  is  J  ^        , 

i      fymnt.  or  thev  are  not 

not  F,  [ 

invert  to 


grant,  or  they  are  not 
white, 


Either  E  may  be  not  ( Either  violets  may  be 
or  E  may  be  not  ^  not  fragrant  or  they 
not-F.  '^     may  be  white. 

Transformations. 

A  is  equal  to  B  or  E  is  equal  to  F 
transforms  to,  e.g., 

B  is  equal  to  A,  or  F  is  equal  to  E. 

XL  Transversions. 

Since  the  elements  of  Hypotheticals,  and  of  the 
Alternatives  which  correspond  to  them,  are  Categori- 
cals,  and  Conditionals  (with  the  corresponding  Alter- 
natives) are  expressible  in  only  such  Categoricals  as 


106  IMMEDIATE  INFERENCES  (EDUCTIONS). 

have  complex  Subject  or  Predicate,  or  both,  it  is  clear 
that  a  simple  Categorical  is  not  reducible  to  Inferen- 
tial or  Alternative  form. 

E.g.  I  am  sorry,  London  is  a  metropolis,  This  man 
is  an  artist.  Genius  is  Patience,  To  err  is  human,  are 
not  susceptible  of  a  simple  and  natural  expression  as 
Inferentials  or  Alternatives.  On  the  other  hand,  all 
Inferential  and  Alternatives  may,  if  desired,  be  ex- 
pressed as  Relative  Categoricals. 

IfA,C    (1) 
is  equivalent  to 

C  /is/  an  inference  from  A. 

Either  C  or  not-A    (2) 

is  equivalent  to 

C  /is/  alternative  with  not-A, 
and  (1)  and  (2)  are  equivalent. 

Conditionals  reduce  to  Absolute  Categoricals  ot  the 

form 

Any  D  that  is  E  is  F. 
Any  D  is  F  or  not  E    (1) 

is  equivalent  to 

Any  D  that  is  E  is  F, 

and  to 

If  any  D  is  E,  it  is  F    (2) 
(2)  may  be  reduced  to  the  Relative  Categorical 

That  any  D  is  F,  is  an  inference  from  its  being  an  E; 
and  (1)  may  be  reduced  to 

That  any  D  is  not  E  is  alternative  with  its  being 

an  F. 


I 


> 
< 


IMMEDIATE  INFERENCES  (EDUCTIONS).  107 


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o 

m 
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t-H 

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IS 


CO 

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pi     CO     ^ 


2?     O     ® 
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I 

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e3 
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1 


SECTION    XL 

INCOMPATIBLE   PROPOSITIONS. 

Propositions  are  Incompatible  when  they  cannot 
both  be  true;  and  while  of  Propositions  related  as 
Educt  and  Educend,  the  first  is  true  if  the  second  is 
true,  of  Propositions  related  as  Incompatibles,  either 
is  false  if  the  other  is  true. 

Propositions  are  generally  said  to  be  Contrary  when 
they  cannot  both  be  true  but  may  both  be  false— e.^. 
All  R  is  Q,  No  R  is  Q ;  Contradictory  when  they  can- 
not both  be  true  and  cannot  both  be  Mse—e.g.  All  R 
is  Q,  Some  R  is  not  Q.    With  Simple  Categoricals,  it 
is  only  where  we  are  concerned  with  Propositions  that 
have  quantified   Subjects   that  Propositions  can  be 
contrarily  opposed.     AU  R  is  Q,  and  No  R  is  Q  seem 
to  be  the  only  Categorical  Contraries  ordinarily  recog- 
nised.   We  do,  of  course,  have  IncompatibiUty  between 
such  Propositions  as 

These  R's  are  Q    (1) 

Some  of  these  R's  are  not  Q    (3) 

These  R's  are  not  Q    (2) 

One  of  these  R's  is  Q    (4) ; 


108 


incompatible  propositions. 


109 


but  the  relation  between  (1)  and  (2),  (1)  and  (3),  (2) 
and  (4)  respectively,  exactly  corresponds  to  that  be- 
tween A  and  E,  A  and  0,  E  and  I.  For  These  R's,  as 
contrasted  with  Some  of  these  R's,  is  equivalent  to  All 
these  Rs.  The  possibility  of  the  two  kinds  of  denial 
(Contrary  and  Contradictory)  depends  upon  the  fact, 
previously  observed,  that  the  Proposition,  All  R  is  Q, 
All  these  R's  are  Q,  etc.,  are  abbreviated  expressions 
for  the  sum  of  a  number  of  Singular  Propositions — 

RMsQ 

R2isQ 

R^  is  Q,  etc. 
A  Proposition  which  sums  up  these  can  of  course 
be  denied  either  by  denial  of  the  whole  series,  or  by 
denial  of  any  one  (or  more)  of  its  constituents. 

In  all  other  cases  a  simple  Categorical  has  but  one 
formal  Categorical  Incompatible,  and  that  one  is  its 
Contradictory — 
fS  is  P 

-  

S  is  not  P 

r  Charles  i.  was  a  saint 

\Charles  i.  was  not  a  saint. 
In  such  a  Proposition  as 

Billy  and  CoHn  are  at  school 
we  have  what  Jevons  calls  a  Compound  Proposition, 
which  is  really  an  abbreviated  expression  of  a  plurality 
of  simple  Propositions.  And  here,  as  in  the  case  of  A 
and  E,  we  may  have  two  Categorical  Incompatibles — 
but  here  both  of  them  are  Contrary — e.g. 


E.g. 


k'^HMiM^'^ 


110 


INCOMPATIBLE  PROPOSITIONS. 


Both  Billy  and  Colin  are  not  at  school    (1) 
Only  one  of  the  two  is  at  school.    (2) 
The  Contradictory  is  obtained  by  a  combination  of 

(1)  and  (2)— 

It  must  be  true  that 

Billy  and  Colin  are  at  school, 

or  that 

One  only  is  at  school  or  neither  is. 

*      Billy  is  at  school  and  in  the  first  class, 
may  be  treated  in  the  same  way. 

The  Conditional  Proposition 

If  any  D  is  E,  that  D  is  F    (1) 
is  certainly  incompatible  with 

If  any  D  is  E,  that  D  is  not  F    (2). 
But  if  the  import  of  (1)  can  be  expressed  by  saying 

That  any  D  is  F  is  an  inference  from  its  being 

an  E, 
then  (1)  and  (2)  do  not  exhaust  all  possibilities ;  for 
it  may  be  that  neither  D  is  F  nor  D  is  not  F  is  an 
inference  from  D's  being  E ;  it  may  be  that  no  con- 
nection is  known  between  Us  being  E  and  Us  being  F. 
(Cf  If  any  dog  is  brown,  that  dog  is  a  spaniel.)  No 
doubt  between  any  two  identities  there  must  be  some 
connection ;  but  (a)  the  connection  may  not  be  such 
as  to  warrant  our  making  any  inference  from  the  one 
to  the  other;    and  (b)  we  may  not  know  what  the 

connection  is. 

We  may  exhibit  Contradictories  of  Class  Categori- 


^x    r  -.^z^^-s 


INCOMPATIBLE  PROPOSITIONS. 


Ill 


cals,  of  Inferential,  and  of  Alternatives  with  the  help 
of  diagrams  as  follows : — 

Let  (1)  (2)  (3)  (4)  (5)  represent  the  possible  relations 
between  A  and  C  (A  and  C  being,  in  the  case  of 
Categoricals,  Class  Names,  of  which  we  are  considering 
the  relative  extent  of  application;  in  the  case  of 
Inferentials  and  Alternatives  being  Propositions,  in 
regard  to  which  we  are  considering  the  relations  of 
inferential  and  alternative  dependence.) 


(1) 


(3) 


(5) 


Then 

All  A  is  C 


n\  f9\    \  ^^  contra-  f     Some  A  is  not  C  (3)  (4) 
^^^  ^"^^    j   dieted  by  \(5). 


112 


INCOMPATIBLE  PROPOSITIONS. 


)  is  contra-  /     Some  A  is   C  (1)  (2)  (3) 
I  dieted  by  \  (4). 

I         „  I     No  A  is  C  (5) 

1  ,,  I     All  A  is  C  (1)  (2). 


No  A  is  C  (5) 

Some  A  is  C  (1) 
(2)  (3)  (4) 

Some  A  is  not  C  (3) 
(4)  (5) 

(1)  or  (2)  are  contraried  by  (3)  or  (4)  or  (5) 

(5)  is  „  „  (1)  or  (2)  or  (3)  or  (4). 

If  A,  C  ( =  If  not  C  ^  is    contra 
not  A)  (1)  (2)  dieted  by 

If  there  is  a  gloomy 
sunset  to-night,  to- 
morrow will  be  wet. 


If     your 


dog 


IS 


l)rown,he  is  a  spaniel. 

If  A,   C   may   be] 
(  =  If  C,  A  may  be) 

(1)  (2)  (3)  (4) 

If  money  go  before, 
some  ways  lie  open 

Either  C  or  not-A\ 
(=Eithernot-AorC) 

(1)  (2) 

Either  the  flower 
in  question  is  scarlet, 
or  it  is  not  a  gera- 
nium. 


11 


f     If  A,  C  may  be  not  (  =  If 

not  C,  A  may  be)  (3)  (4)  (5). 

Though   we  may  have  a 
gloomy    sunset  to-night,   it 
J  does    not    follow    that    to- 
morrow will  be  wet. 

Though  my  dog  is  brown, 
it  does  not  follow  that  he  is 
a  spaniel. 

If  A,  not-C  (  =  If  C,  not 

A)  (5). 


?? 


?i 


Though  money  go  before, 
no  ways  lie  open. 

/     Either  not- A,  or  [if  A]  C 
may  be  not ;  Neither  C  nor 

not-A  (3)  (4)  (5). 

The  flower  in  question  may 
be  not  scarlet  though  a  gera- 
nium ;  the  alternative  to  the 
flower's  being  scarlet  need 
not  be  that  it  is  not  a  gera- 
nium ;  the  flower  may  be 
neither  scarlet  nor  not  a  gera- 
nium. 


INCOMPATIBLE  PROPOSITIONS. 


113 


Either  A  or  uot-C 
(2)  (3). 

He  must  submit  or 
he  will  be  ruined. 

It  is  either  knavery 
or  folly. 

He  has  not  done  it, 
or  he  deserves  to  go 
to  prison. 

Either  A  may  be 
or  C  is  not  (  =  Either 
C  niav  be  or  A  is  not) 

(1)  (2)  (3)  (4). 


is  contra- 
dicted by 


)) 


M 


?1 


?) 


H 


Either  C  is  not,  or  not-A 
is  possible  ;  Neither  A  nor 

not-C  (1)  (4)  (5). 

His  submission  and  his 
ruin  are  not  alternatives. 

It  may  be  neither  knavery 
nor  follv. 

He  mav  have  done  it  and 
yet    not   deserve    to   go    to 
V  prison. 

Neither  C  is  not  nor  may 
A  be  (  =  Neither  is  A  not, 
nor  may  C  be) ;  Either  not-C 
or  not-A  (5). 


gMiaiaBma^i^ 


CATEGORICAL  MEDIATE  INFERENCES. 


115 


SECTION    XII. 

CATEGORICAL  MEDIATE  INFERENCES. 

In  Mediate  Inferences  or  Arguments,  the  Inference 
is  drawn  from  two  Propositions  taken  together,  which 
are  called  the  Premisses.  In  Categorical  Mediate 
Inferences  the  Conchision  and  both  Premisses  are 
Categorical  Propositions,  Categorical  Mediate  Infer- 
ences may  be  divided  into  Absolute  Arguments  or 
Syllogisms,  and  Relative  Arguments. 

A  Categorical  Argument  may  be  defined  as— 
A  combination  of  three  Categorical  Propositions, 
one  of  which  (the  Conclusion)  is  inferred  from 
the  other  two  taken  together— these  two  being 
called  the  Premisses. 

A  Categorical  Syllogism  is  a  Categorical 
Argument,  of  which  the  Premisses  have  in 
common  one  Term-name  which  does  not  occur 
in  the  Conclusion.  The  Conclusion  has  its 
S-name  in  common  with  one  Premiss,  and  its 
P-name  in  common  with  the  other  Premiss. 

114 


A  Syllogism  as  thus  defined  may  have  five  Terms, 
but  can  have  only  three  Term-names  (of,  p.  10). 
E.g,  in 

(a)    AUNisQ 

(h)    All  R  is  N 

(c)  Some  R  is  Q 
the  Terms  are  (1)  All  N,  (2)  [Some]  N,  (3)  All  R,  (4) 
Some  R,  (5)  [Some]  Q;  the  Term-7iames  are  (1)  R, 
(2)  N,  and  (3)  Q.  In  the  above  Syllogism,  All  N  and 
[Some]  N  are  Middle  Terms,  All  R  and  Some  R  are 
Minor  Terms,  and  [Some]  Q  is  Major  Term.  [Some] 
N  of  course  coincides,  ex  vi  termini  with  part  (at 
least)  of  All  N,  and  it  is  this  part  of  All  N  that  is  the 
real  medium  of  connection  between  Major  and  Minor 
Terms. 

The  Middle  Term,  then,  in  either  Premiss  of  a 
Syllogism,  is  that  which  has  the  Term-name  common 
to  both  Premisses. 

The  Major  Term  in  the  Premisses  of  a  Syllogism  is 
that  which  has  its  Term-name  in  common  with  the  P 
of  the  Conclusion;  and  the  Major  Premiss  is  the 
Premiss  which  contains  the  Major  Term. 

The  Minor  Term  in  the  Premisses  of  a  Syllogism  is 
that  which  has  its  Term-name  in  common  with  the  S 
of  the  Conclusion;  and  the  Minor  Premiss  is  the 
Premiss  which  contains  the  Minor  Term. 

In  the  Syllogism  given  above,  (a)  is  the  Major 
Premiss,  (b)  is  the  Minor  Premiss,  and  (c)  is  the  Con- 
clusion. 


liliftiiillfiimiffliflfriiinili 


116  CATEGORICAL  MEDIATE  INFERENCES. 

The  Canon  of  Categorical  Syllogisms  (as  thus 
defined)  may  be  stated  as  follows  :— 

If  the  Application  of  any  two  Terms  is  identical  (or 
distinct),  any  third  Term  which  has  a  different 
Term-name,  and  is  identical  in  AppUcation 
with  the  whole  (or  part)  of  one  of  those  two,  is 
also  (in  whole  or  part)  identical  with  the  other 
(or  distinct  from  it). 

To  take  examples  of  the  most  generaUsed  form  of 
Categorical  Syllogism— in 

MisP 
SisM 


SisP 


the  two  Terms  M  and  P  have  identical  application ;  a 
third  Term,  S,  is  identical  in  Application  with  M; 
therefore  S  is  identical  with  P. 


In 


M  is-not  P 
SisM 


S  is-not  P 
the  two  Terms  M  and  P  have  distinct  Application— 
what  M  applies  to  is  other  than  (not  identical  with) 
what  P  applies  to ;  but  a  third  Term,  S,  is  identical  in 
AppUcation  with  M,  therefore  it  is  distinct  from  that 
which  M  is  distinct  from,  namely  P. 

In  the  case  of  Categorical  Class  Syllogisms,  the 
application  of  the  Canon  may  be  iUustrated  by  taking 


SSi-rt«— n?'SK^:-W7^?--"*'-*«rSW,^'' 


categorical  mediate  inferences.  117 

the  following  examples  expressed  in  symbols.    In 
(No  N)  is  (Q) 
(All  R)  is  (N) 

(No  R)  is  (Q) 

the  Application  of  (1)  All  N  is  other  than  the  Appli- 
cation of  (2)  [All]  Q ;  and  the  AppUcation  of  (3)  All 
R  is  identical  with  some  of  the  Application  of  All  N ; 
hence  All  R  is  other  than  [All]  Q. 
In 

(All  Q)  is  (N) 

(No  R)  is  (N) 

(No  R)  is  (Q) 

the  Application  of  (1)  All  R,  is  different  from  that  of 
(2)  [All]  N ;  the  Application  of  (3)  All  Q,  is  identical 
with  some  of  the  Application  of  [All]  N ;  hence  the 
Application  of  All  R  is  other  than  the  Application  of 
[All]  Q. 
In 

(All  N)  is  (Q) 

(All  N)  is  (R) 

(Some  R)  is  (Q) 

the  Application  of  (1)  All  N  is  identical  in  Applica- 
tion with  (2)  [Some]  Q ;  the  Application  of  (3)  [Some] 
R  is  identical  with  the  application  of  All  N ;  hence 
the  Application  of  Some  R  is  identical  with  the  Ap- 
plication of  [Some]  Q. 

The  following  Rules  secure  the  applicability  of  the 
Canon,  and  the  exclusion  of  all  invalid  Syllogisms : — 


118 


CATEGORICAL  MEDIATE  INFERENCES. 


Rule  I. — In  every  Syllogism,  the  Application  of  the 
Middle  Term  in  one  Premiss  must  be  identical  with 
the  whole,  or  a  part,  of  the  Application  of  the  Middle 
Term  in  the  other  Premiss.^ 

Rule  IL— The  Application  of  the  Major  Term  and 
the  Minor  Term  in  the  Conclusion  must  be  identical 
with  the  whole,  or  a  part,  of  the  Application  of  the 
Major  and  Minor  Tenns  respectively  in  the  Premisses.^ 
Rule  III.— Identity  of  AppHcation  of  the  Terms  in 
the  Conclusion  requires  Identity  of  Application  in 
both  Premisses ;  and  Otherness  of  Application  of  the 
Terms  in  the  Conclusion  requires  Otherness  of  Ap- 
pHcation of  the  Terms  in  one  (but  only  one)  Premiss. 

From  any  pair  of  Premisses  in  which  there  is  a 
breach  of  Rule  I.,  no  Mediate  Inference  can  be  dra^vn ; 
since  any  breach  of  Rule  I.  involves  the  absence  of  a 
true  Middle-Term— that  is,  it  involves  the  absence  of 
complete  or  partial  coincidence  of  Application  between 
one  Term  (and  one  Term  only)  in  one  Premiss,  and  one 

1  By  Obversion  of  either  Premiss,  which  has  the  Middle  Term  for 
Predicate,  these  corresponding  Terms  in  the  two  Premisses  may  be 
made  absolutely  distinct.     E.g. — 

AllQisN    (1) 
No  R  is  N     (2) 
by  Obversion  of  (2)  becomes 

All  Q  is  N 
All  K  is  not-N. 

2  By  Obversion  of  the  Conclusion,  the  Application  of  the  Major 
'    Term  in  the  Conclusion  may  be  made  absolutely  distinct  from  the 

Application  of  the  corresponding  Term  in  the  Premisses ;  and  by 
Obversion  of  the  Minor  Premiss  (when  the  Minor  Term  is  Predicate 
in  its  Premiss),  the  Minor  Term  in  the  Conclusion  is  made  the 
negative  of  the  Minor  Term  in  the  Premisses. 


CATEGORICAL  MEDIATE  INFERENCES. 


119 


Term  in  the  other  Premiss  (without  which  there  is 
no  such  connection  between  the  Premisses  as  makes 
it  possible  to  draw  a  conclusion  from  them  taken 
together).  Where  there  is  a  breach  of  Rule  IL,  or  of 
Rule  III.,  the  Conclusion  is  not  that  which  ought  to 
be  inferred  from  the  Premisses  taken  together ;  and 
there  is  {a)  Illicit  Process  of  the  Major  Term,  or  (b) 
Illicit  Process  of  the  Minor  Term,  or  (c)  more  than 
three  Term-names  in  the  Premisses,  together  with  the 
Conclusion  (and  in  all  these  cases  there  is  a  redund- 
ancy of  Terms  in  Premisses  -f  Conclusion) ;  or  finally, 
((/)  one  Premiss  is  repeated  or  inferred  from  (and  in 
this  case  there  is  the  fault  of  Tautology). 

The  following  pairs  of  Propositions  illustrate  breaches 
of  Rule  I. — from  none  of  them  can  any  Mediate  Infer- 
ence be  drawn  as  Conclusion  : — 

All  R  is  Q  K  is  L  Some  N  is  Q 

Some  R  is  ^  T  is  Y  Some  N  is  R 

All  angels  are  good  spirits 

All  angels  are  coins  worth  ten  shillings. 

The  following  Syllogisms  illustrate  breaches  (a),  (6), 
(c),  {d)  of  Rules  II.  and  III. : — 
(«)AllNisQ    (6)  All  N  is  Q 
Some  R  is  N       No  R  is  N 
All  R  is  qT       No  R  is  Q. 
(c)  All  N  is  Q     (r/)  These  statesmen  are  authors 
All  R  is  N  These  statesmen  are  musicians 

All  X  is  Q.  Some  musicians  are  statesmen. 


120 


CATEGORICAL  MEDIATE  INFERENCES. 


In  Deductions  in  which  all  the  Subject-Terms  are 
Individual  or  Partial,  and  have  the  same  extent  of 
Application,  and  in  all  quantiticated  Categorical  Syl- 
logisms, it  is  not  of  essential  consequence  which 
Premiss  is  Major  or  Minor,  nor  which  Term  is  S  and 
which  P,  in  any  of  the  three  constituent  Propositions. 
But  in  dealing  with  unquantificated  Class  Categoricals, 
both  these  points  are  of  essential  importance,  since 
transposition  of  Terms  or  Propositions  may  be  im- 
possible, or  may  destroy  the  validity  of  a  Syllogism. 
E.g.  in 

London  is  the  capital  of  England 

London  is  the  largest  city  in  the  world 

The  capital  of  England  is  the  largest  city  in 
the  world, 
we  may  alter  the  order  of  Terms  and  of  Propositions 
without  destroying  the  validity  of  the  Syllogism,  or 
essentially  affecting  the  meaning  conveyed  by  it. 
And  of  such  a  Syllogism  as 

The  '  Syndics '  and  '  Night  Watch '  are  some 

of  Kembrandt's  masterpieces 
The  'Syndics'  and  'Night  Watch'  are  two 
of  the  pictures  in   the  new  Museum  at 

Amsterdam 

Two  of  the  pictures  in  the  new  Museum  are 
some  of  Rembrandt's  masterpieces, 

we  may  say  the  same.    But  if  we  take  a  Class  Syllogism 
such  as  the  following — 


CATEGORICAL  MEDIATE  INFERENCES.  121 

All  Planets  are  heavenly  bodies    (1) 
No  Planets  are  self-luminous        (2) 

Some  heavenly  bodies  are  not  self-luminous  (3), 

and  put  (2)  for  Major  Premiss  and  (1)  for  Minor  Pre- 
miss, this  necessitates  conversion  of  (3) — since  the  P 
of  the  Conclusion  must  be  the  Major  Term,  and  the 
S  of  the  Conclusion  must  be  the  Minor  Term — but 
(3)  being  an  0  Proposition,  is  inconvertible. 

And  if  we  take  as  the  Premisses  of  an  AAA 
Syllogism  the  following  two  propositions — 

All  Carnivora  are  fierce     (1) 
All  Lions  are  Carnivora     (2) 

we  find  that  with  (1)  for  Major  Premiss  and  (2)  for 
Minor  Premiss  we  get  a  valid  Conclusion  in  A,  i.e. — 

All  Lions  are  fierce. 

But  with  (2)  for  Major  Premiss  and  (1)  for  Minor 
Premiss,  our  Conclusion,  if  A,  must  be — 

All  fierce  creatures  are  Lions, 
which  is  invalid ;  and  if  the  Conclusion  is  I,  i.e. — 

Some  fierce  creatures  are  Lions — 
the  Syllogism  is  valid,  but  it  is  not  AAA  (in  Fig.  i.) 
but  AAI  (in  Fig.  iv.). 

Hence  it  is  necessary  to  consider  the  different 
Figures  and  Moods  of  Class  Syllogisms,  and  in  con- 
nection with  them,  the  Reduction  of  one  Syllogistic 
Mood  to  another. 

By  Mood  is  meant  the  form,  and  order  of  the  Pro- 


ts' 


122 


CATEGORICAL  MEDIATE  INFERENCES. 


CATEGORICAL  MEDIATE  INFERENCES. 


123 


positions  which  go  to  make  up  a  Syllogism— thus  the 
Mood  EAE  (e.g.  cEsArE)  refers  to  a  Syllogism  con- 
sisting of  an  E  Major   and  Conclusion,  and  an   A 

Minor. 

By  Figure  is  meant  the  order  of  Terms  in  the  Pre- 
misses of  a  Syllogism.  Since  this  may  vary  in  four 
ways,  there  are  four  figures  of  Syllogism,  called 
respectively  the  First,  Second,  Third,  and  Fourth 
Fi2fures,  as  follows  : — 

Fig.  III.         Fig.  IV. 
M-P  P-M 

M-S  M-S 


Fig.  I. 
M-P 

S-M 


Fig.  II. 
P-M 
S-M 


Of  Class  Syllogisms  only  AAA  (AAI),  EAE 
(EAI),  All,  and  EIO  are  valid  Moods  in  Fig.  i.; 
only  EAE  (EAO),  AEE  (AEG),  EIO,  AOO,  in 
Fig.  II.;  only  AAI,  lAI,  All,  EAO,  in  Fig.  in.; 
and   only   AAI,   AEE  (AEO),   lAI,   EAO,   EIO,    in 

Fig.  IV. 

In  Fig.  I.  and  Fig.  iii.  the  Major  Premiss  and  the 
Conclusion  may  be  Adjectival  Propositions  (of.  ante, 
pp.  14,  15),  but  the  Minor  Premiss  cannot;  and  in 
Fig.  II.  and  Fig.  iv.  neither  of  the  Premisses,  nor  the 
Conclusion,  can  be  Adjectival. 

An  ancient  verse  of  logical  Mnemonics  contains 
the  technical  names  of  nineteen  of  these  'Moods' 
(the  five  Moods  in  brackets  being  weakened  forms  of 
the  Syllogisms  which  they  follow— that  is,  having  a 
Particular  Conclusion  when  the  corresponding  Uni- 


versal is  justified  by  the  Premisses).  The  verse 
furnishes  at  the  same  time  a  key  by  which  the  un- 
weakened  Moods  of  Figs,  ii.,  in.,  and  iv.  may  be 
reduced  to  unweakened  Moods  of  Fig.  i.  Keduction 
to  Fig.  I.  was  thought  useful  because  it  was  regarded 
as  the  most  perfect  Figure,  the  Figure  to  which  alone 
the  Dictum  de  omni  et  nullo^  applies  directly,  in 
which  the  argument  is  most  obviously  valid,  and  in 
which  the  S  and  P  of  the  Conclusion  occur  as  S  and 
P  in  their  respective  Premisses.  The  verse  referred 
to  is  as  follows : — 

Barbara,  Celarent,  Darii,  Ferio  que  prioris ; 
Cesare,  Camestres,  Festino,  Baroko,  secundae ; 
Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 
BoKARDO,  Ferison  habct ;  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

The  words  in  capital  letters  are  the  names  of  the 
valid  Moods  in  the  four  Figures  respectively;  the 
initial  letters  of  the  names  in  the  2nd,  3rd,  and  4th 
Figures  correspond  to  the  initial  letters  of  the  names 
in  the  1st  Figure,  and  every  inferior 'Mood  reduces  to 
the  Mood  in  Fig.  i.,  which  begins  with  its  own  letter ; 
e.g.  Cesare  (in  Fig.  ii.)  reduces  to  Celarent.  The 
letter  m  wherever  occurring,  signifies  transposition 
of  Premisses ;  e.g.  in  reducing  Camestres  to  Celarent, 
the  Premisses  are  transposed.     The  letters  s  and  p 

1  This  Dictum— the  traditional  Canon  of  Syllogism— may  be  stated 
as  follows  :—  Whatever  may  be  predicated  of  a  term  distributed,  may 
he  predicated  in  like  manner  of  everything  contained  under  it. 


124 


CATEGORICAL  MEDIATE  INFERENCES. 


signify  Conversion  (Conversion  >Siimpliciter  and  Con- 
version Per  Accidens) ;  e.g.  in  reducing  Camestres  to 
Celarent  the  Minor  Premiss  and  the  Conclusion  are 
converted,  in  reducing  Darapti  to  Darii,  the  Minor 
Premiss  is  converted. 

The  vowels  of  the  Mood-names  signify  the  kind  of 
Class  Propositions  of  which  each  Mood  is  composed ; 
e.g.  Ferio  has  E  for  Major  Premiss,  I  for  Minor 
Premiss,  and  0  for  Conclusion.  The  only  remaining 
significant  letter  in  the  verses  is  K,  which  occurs  in 
two  names,  Baroko  and  Bokardo ;  this  K  signifies 
Indirect  Reduction,  which  will  be  explained  and  ex- 
emplified further  on. 

The  Reductions  of  the  other  Moods,  for  which  the 
Mnemonic  verse  supplies  a  key,  are  Direct  or  Osten- 
sive,  and  consist  simply  in  Transposition  of  Premisses 
or  of  Terms. 

The  name  Bramantip  requires  special  explanation. 
By  transposition  of  the  Premisses  of  this  Mood,  and 
Conversion  of  the  Conclusion,  we  reach  (not  AAA 
but)  AAI  in  Fig.  i.,  which  is  Barbara  with  a  weakened 
Conclusion,  that  is,  with  an  I  Conclusion  when  an  A 
Conclusion  would  have  been  justified  by  the  Pre- 
misses— but  this  A  Conclusion  would  not  be  justifiable 
as  an  Immediate  Inference  from  the  I  Conclusion  of 
Bramantip.  The  jp  of  this  name  must  be  understood 
to  indicate  that  if  we  took  Barbara  exactly  as  it 
stands  in  Fig.  i.,  and  converted  the  Conclusion 

All  R  is  Q,  we  should  get  Some  Q  is  R, 


CATEGORICAL  MEDIATE  INFERENCES. 


125 


which  is  the  Conclusion  of  Bramantip  when  reduced 
to  Fig.  I. 

We  will  go  through  the  unweakened  Moods  of 
Fig.  II.,  Fig.  III.,  and  Fig.  iv.,  exhibiting  in  each  case 
the  Reduction  to  Fig.  i. 


Cesare 
No  Q  is  N 
jm  R  is  N 

No  R  is  Q 

Camestres 
AllQisN 
No  R  is  N 
No  R  is  Q 

Festino 

No  Q  is  N 
Some  R  is  N 

Some  R  is-not  Q 

Darapti 
All  N  is  Q 
All  N  is  R 

Some  R  is  Q 

Disamis 
Some  N  is  Q 
AllNisR 

Some  R  is  Q 


reduces  to 


i> 


yi 


» 


n 


Celarent. 
NoNisQ   (M-PtoP-M) 

AU  R  is  N 

No  R  is  Q. 

Celarent. 
No  N  is  R 
All  Q  is  N 

No  Q  is  R 

Ferio. 
No  N  is  Q 
Some  R  is  N 
Some  R  is-not  Q. 

Darii. 
AllNisQ  (M-StoS-M) 
Some  R  is  N 
Some  R  is  Q. 

Darii. 

AU  N  is  R 

Some  Q  is  N 

Some  Q  is  R. 


126 


CATEGORICAL  MEDIATE  INFERENCES. 


CATEGORICAL  MEDIATE   INFERENCES. 


127 


Datisi 

All  N  is  Q 
Some  N  is  R 

Some  R  is  Q 

Felapton 

No  N  is  Q 
All  N  is  R 


reduces  to 


Some  R  is-not  Q 

Ferison 

-No  N  is  Q 
Some  N  is  R 

Some  R  is-not  Q 

Bramantip 
AH  Q  is  N 
All  N  is  R 
Some  R  is  Q 


Camenes 

AU  Q  is  N 
NoJs^]sR 

NoRisQ 

Dimaris 
Some  Q  is  N 
All  N  is  R 


Some  R  is  Q 


y> 


jt 


it 


it 


n 


Darii. 

All  N  is  Q 
Some  R  is  Q 
Some  R  is  Q. 

Ferio. 

No  N  is  Q 
Some  R  is  N 


Some  R  is-not  Q. 

Ferio. 

No  N  is  q 
Some  R  is  N 

Some  R  is-not  N. 

Barbara. 

AUNisR  (P-MtoM-P) 
AllQisN  (M-StoS-M) 

« 

Some  Q  is  R 
(Cf.  ante,  1^.124^.) 

Celarent. 
No  N  is  R 
All  Q  is  N 
No  Q  is  R. 

Darii. 

All  N  is  R 
Some  Q  is  N 


Some  Q  is  R. 


Fesapo 

No  Q  is  N 
AU  N  is  R 


reduces  to 


Some  R  is-not  Q 

Fresison 
No  Q  is  N 
Some  N  is  R 
Some  R  is-not  Q 


» 


Ferio. 
No  N  is  Q 
Some  R  is  N 

Some  R  is-not  Q. 

Ferio. 
No  N  is  Q 
Some  R  is  N 
Some  R  is-not  Q. 


Baroko  and  Bokardo,  as  already  mentioned,  are 
reduced  by  a  different  process  (called  Indirect  Reduc- 
tion or  Redwctio  ad  impossihile)  to  Barbara,  and  this 
process  is  indicated  by  the  K  which  occurs  in  them 
only.  This  Indirect  Reduction  is  as  follows  : — 
We  take,  say,  Baroko — namely. 

All  Q  is  N  2  ^  "^  ti  , 

Some  R  is-not  N  I  iJ  ^       h/  i 


Some  R  is-not  Q — 
and  make  the  supposition  thajt  tnte  ConcTiision,  Some 
R  is-not  Q,  is  to  be  questioned,  not  because  the  Pre- 
misses are  doubted,  but  because  this  form  of  Syllo- 
gism is  supposed  to  be  less  trustworthy  than  the 
First  (and  '  perfect ')  Figiu'e.  If  Some  R  is-not  Q,  is 
not  true,  then  its  Contradictory  All  R  is  Q,  must  be 
true.  Let  us  take  this  as  a  Premiss  in  a  new  Syllo- 
sfism,  and  take  one  of  the  Premisses  of  Baroko  for  the 
other  Premiss,  thus — 

All  Q  is  N 

All  R  is  Q. 


128 


CATEGORICAL  MEDIATE  INFERENCES. 


These  Premisses  yield  the  Conckision 

All  R  is  N. 
But  All  R  is  N  contradicts  Some  R  is-not  N,  the 
Minor  Premiss  of  Baroko,  and— by  supposition— the 
Premisses  of  Baroko  were  not  to  be  questioned.     As, 
however,  the  new  SyUogism  is  in  the  First  Figure,  we 
cannot  doubt  that  the  Conclusion  is  rightly  deduced 
from  the  Premisses.     The  fault,  therefore,  must  be  in 
the  Premisses  of  the  new  Syllogism.     But  All  R  is  N 
(being  one  of  the  original  Premisses)  is  right.     There- 
fore it  must  be  the  Premiss  All  R  is  Q  which  is  at 
fault.     Therefore  All  R  is  Q  must  be  false.    Therefore 
its  Contradictory  must  be  true.     Therefore  Some  R 
is-not  Q  is  right,  and  Baroko  is  proved  to  be  vaUd. 

The  reasoning  in  the  case  of  Bokardo  proceeds  in 
precisely  the  same  manner.     Bokardo — 
Some  N  is-not  Q 
All  N  is  R 
Some  R  is-not  Q — 
reduces  indirectly  to 
All  R  is  Q 
All  N  is  R 
All  N  is  Q. 
But  All  N   is  Q  contradicts  the  Major  Premiss  of 
Bokardo,  therefore  the  new  Syllogism  is  wrong,  there- 
fore the  old  Syllogism  is  right. 

Baroko  and  Bokardo,  however,  can  be  reduced 
ostensively  by  the  help  of  Obversion  and  Contraver- 
sion,  thus : — 


CATEGORICAL  MEDIATE  INFERENCES.  129 

Baroko— All  P  is  M    (1) 

Some  S  is  not  M     (2) 
Some  S  is  not  P    (3) — 
reduces  to 

No  not-M  is  P  .  .  .  .  contraverse  of  (1)     ^ 
Some  S  is  not-M .  .  .  obverse  of  (2) 
Some  S  is-not  P. 

This  is  Ferio  in  Fig.  i.,  and  we  may  take  the  name 
Faksoko  as  a  key,  understanding  k  to  mean  Obver- 
sion, and  s  (as  before)  to  mean  Conversion. 
Bokardo — Some  M  is  not  P  (1) 
AUMisS     (2) 
Some  S  is  not  P     (3)— 

reduces  to  a  Syllogism  in  Darii,  namely, 

AUMisS    (2) 

Some  not-P  is  M .  .  .  contraverse  of  (1) 

Some  not-P  is  S  .  .  .  contraverse  of  (3) 

This  may  be  symbolised  by  the  verbal  combination 
Doksmanoks,  k  having  the  same  meaning  as  in 
Faksoko,  and  s  and  m  retaining  the  signification 
which  they  have  in  the  other  Mnemonic  names. 

Relative  Categorical  Arguments  are  Arguments  of 
which  the  Premisses  are  Relative  Propositions ;  they 
do  not — like  Syllogisms — conform  to  one  strict  and 
invariable  pattern;  and  the  Canon  and  Rules  of 
Syllogism  will  not  apply  directly  to  them — but  their 
cogency  (to  any  one  who  understands  the  relations  of 

I 


■seffiiSiMteVtiiiiiiiifiMiffiMiaiaaii 


130  CATEGORICAL  MEDIATE  INFERENCES. 

the  System  they  refer  to)  is  just  as  evident  as  that  of 
Syllogistic  or  Absolute  Arguments.  It  is,  moreover, 
possible  to  express  them  in  Syllogistic  form(c/.  p.  37). 
Take,  for  instance,  the  following  Kelative  Argument 
(which  is  of  the  particular  species  called  A  fortiori)— 

A  /is/  greater  than  B 
B  /is/  greater  than  C 
A  /is/  greater  than  C. 


Here  we  have  four  Term-names,  but  yet  a  perfectly 
valid  argument— that  which  takes  the  place  of  a  true 
Middle  Term,  and  supplies  the  point  of  connection 
between  A  and  C,  being  B;  which,  as  the  Premisses 
imply,  is  at  the  same  time  greater  than  C  and  less 
than  A  {A  is  greater  than  B  being  equivalent  to  B  is 
less  than  A).  The  Premisses  give  us  not  only  a  state- 
ment of  two  identities,  but  also  information  as  to  the 
relations  of  three  distinct  objects— A,  B,  and  C. 

The  Argument  may  be  expressed  syllogistically  as 

follows: — 

(A  thing  which  is  greater  than  a  second  thmg 
which  is  greater  than  a  third  thing)  is  (greater 
than  that  third  thing) 


CATEGORICAL  MEDIATE  INFERENCES. 


131 


(This  thing  [A])  is  (greater  than  a  second  thing 
[B]  which  is  greater  than  a  third  thing  [C]) 

.-.  (This  thing  [A])  is  (greater  than  the  third  thing 

Take,  again,  the  Argument 
X  is  equal  to  Y 
Y  is  equal  to  Z 
X  is  equal  to  Z 


Here,  again,  we  have  four  Term-names,  and  three 
distinct  objects  referred  to,  one  of  which  fulfils  the 
function  of  a  Middle  Term  by  affording  a  point  of 
connection  between  the  other  two  objects. 

The  Argument  may  be  put  syllogistically  as 
follows : — 

Any  thing  that  is  equal  to  another  thing  (Y)  /is/ 

equal  to  what  Y  is  equal  to  (Z) 
This  thing  (X)  /is/  equal  to  another  thing  (Y) 

This  thing  (X)  /is/  equal  to  what  Y  is  equal  to  (Z), 

If  any  X  is  equal  to  Y,  that  X  /is/  equal  to  Z 

that  Y  is  equal  to 
This  X  is  equal  to  Y ' 

This  X  /is/  equal  to  Z  that  Y  is  equal  to. 


or 


JliffciiliiHiWtiiitlffntiliiiTdtiBitiirj^^ 


182 


CATEGORICAL  MEDIATE  INFERENCES. 


Other  arguments  of  a  similar  nature  are  those  in 
which  the  Systems  of  relations  referred  to  by  the  con- 
stituent Propositions  are  relations  of  time,  of  family 
connection,  of  position  in  space,  and  so  on.     E.g. — 

A  is  father  of  B 

B  is  father  of  C 

C  is  grandson  of  A. 
Here  we  have  six  terms,  but  still  three,  and  only 
three,  related  objects,  one  of  which,  B,  affords  the 
point  of  connection  between  the   two  others.     The 
argument  is  perfectly  cogent  and  perfectly  evident— 


A-B-C 


A  is  to  the  left  of  B 
B  is  to  the  left  of  C 


C  is  to  the  right  of  A 
is  a  similar  Argument. 

It  does  not  appear,  on  this  view,  that  we  can  get  a 
more  precise  Canon  of  Relative  Categorical  Mediate 
Inferences  than  the  following  :— 

If  two  objects,  A  and  B,  are  related  to  each  other, 
and  B  is  related  to  a  third  object,  C ;  then  C  is  related 
to  A  in  accordance  with  the  laws  of  the  System  to 
which  A  and  B  and  C  belong. 


SECTION    XIII. 


INDUCTIONS. 


Categorical  Mediate  Inferences,  whether  Syllo- 
gistic or  Relative,  may  be  divided  into  Deductions  and 
Inductions  (c/.  Section  ix.,  on  Inferences  in  General). 
These  two  kinds  of  argument  are  similar,  but  not  pre- 
cisely similar.  Take  the  following  instances  of  Deduc- 
tive Arguments : — 

(1)  London  is  the  largest  city  in  the  world 
London  is  the  metropolis  of  England 

The  metropolis  of  England  is  the  largest  city 
in  the  world. 

(2)  Those  two  fowls  are  worth  ten  shillings  each 
Those  two  fowls  are  Silver  Hamburghs 
Some    Silver    Hamburghs    are    worth    ten 

shillings  each. 

(3)  All  horned  animals  are  ruminants 
All  cows  are  horned  animals 

All  cows  are  ruminants. 

(4)  All  white  violets  are  fragrant 
This  flower  is  a  white  violet 


This  flower  is  fragrant. 


133 


- 1 


134 


INDUCTIONS. 


(5)  Spring,  Summer,  Autmnn,  and  Winter  make 
up  a  year 
Spring,   Summer,  Autumn,  and  Winter   are 

the  four  seasons 
The  four  seasons  make  up  a  year. 
In  none  of  these  do  we  find  that  the  Conckision  is 
more  general  than  either  of  the  Premisses.  And 
among  the  most  important  of  Deductive  Arguments 
are  those  which — as  (3)  and  (4) — start  from  the  asser- 
tion of  laws  or  general  statements,  and  combine  two 
such  to  reach  the  Conclusion,  or  apply  one  law  to 
some  particular  case  or  cases. 

In  an  Induction,  on  the  other  hand,  Ave  have  always 
one  Premiss  Particular  and  the  Conclusion  Universal 
— we  arrive,  by  the  help  of  facts  or  particulars,  at 
some  fresh  generalisation  or  law.  For  instance, 
having  proved  that  one  isosceles  triangle  has  the 
angles  at  the  base  equal,  we  conclude  that  all  isosceles 
triangles  have  the  angles  at  the  base  equal;  having 
ascertained  that  one  rabbit  has  died  from  the  admini- 
stration of  a  certain  quantity  of  arsenic,  we  conclude 
that  any  rabbit  would  die  in  consequence  of  a  similar 
dose ;  having  observed  that  one  bunch  of  fresh  white 
violets  has  a  particular  fragrance,  we  infer  that  other 
bunches  of  the  same  fresh  flower  will  have  a  similar 
fragrance.  But  our  Inferences  cannot  be  of  the  form. 
This  isosceles  triangle  has  the  angles  at  the  base 
equal 
.'.All  isosceles  triangles  have  the  angles  at  the  base 


INDUCTIONS. 


135 


equal — and  so  on ;  for  if  so  they  would  be  not  Mediate 
but  Immediate  Inferences,  and,  moreover,  illegitimate 
Immediate  Inferences.  We  must  have  two  Premisses, 
of  which  one  is  a  Universal  Proposition;  and  this 
Universal,  together  with  the  Particular  Premiss,  must 
furnish  a  complete  justification  for  the  Conclusion. 

Why  is  it  that  I  feel  justified  in  inferring  from  the 
one  isosceles  triangle  to  all  isosceles  triangles,  from 
the  one  rabbit  dosed  with  arsenic  to  all  rabbits  dosed 
with  arsenic,  from  the  one  bunch  of  violets  to  all 
bunches  ?     It  would  appear  that  the  justification  is  to 
be  found  in  what  may  be  called  the  Principle  of  Inter- 
dependence.    This  Principle  may  be  stated  thus — 
Every  characteristic  (cf.  pp.  5,  6),   is   inseparable 
from  some  other  characteristics ;  and  there  is 
an    iiniformity    of  interdependence  between 
characteristics. 
I  use  Interdependence  to  mean  inseparable  co-exist- 
ence (Concomitance)  or  inseparable  antecedence  or 
consequence  (Cause  and  Effect) ;  and  the  Principle  of 
Interdependence  as  above  stated  may  be  amplified  as 
follows : — 

Every  characteristic  of  anything  has  some  Con- 
comitants, and  every  change  or  event  has  some  Cause 
and  some  Effect;  moreover,  not  only  is  there  this 
connection  in  any  given  case,  but  the  connection  is 
uniform — that  is,  not  only  must  every  characteristic 
be  inseparable  from  some  other  characteristics,  but  it 
is  similar  characteristics  that  are  interdependent — 


136 


INDUCTIONS. 


i.e.  phenomena  that  are  once  connected  as  Concomi- 
tants, or  Cause  and  Effect,  are  always  so  connected. — 
An  Inductive  Mediate  Inference  will  therefore  be  of 
the  form 

Whatever  has  once  been  a  cause  of  Y  will  be 

always  a  cause  of  Y 
X  has  been  once  a  cause  of  Y 

X  will  be  always  a  cause  of  Y  ( =  All  X  is 
cause  of  Y) — 


or 


Any  characteristics  that  are  once  concomitant 
with  A  will  be  always  concomitant  with  A 
BC  are  once  concomitant  with  A 


BC  will  be  always  concomitant  with  A  ( =  All 
BC  are  concomitant  with  A). 

And  it  seems  clear  that  Uniformity  of  Causation  must 
depend  upon  Uniformity  of  Concomitance — our  power 
of  predicting  that  one  event  A  will  be  followed  by 
another  event  B  must  depend  wholly  upon  co-existence 
of  characteristics  in  the  Subjects  concerned — event 
meaning  change  in  Subjects  of  Attributes.  (The  above 
Inductive  Inferences  can  be  equally  well  expressed  in 
Inferential  form— their  expression  in  Alternative  form 
is  awkward  and  inappropriate.) 

If  we  have  seen  one  animal  dosed  with  arsenic 
and  subsequently  die,  and  hence  conclude  that  an- 
other animal  called  by  the  same  name,  and  dosed 
with  an  equal  amount  of  arsenic,  will  die,  is  not  our 
inference  based  upon  the  assumption  of  a  certain  con- 


INDUCTIONS. 


137 


stant  coinherence  of  characteristics,  both  in  the  animal 
and  in  the  poison — a  coinherence  of  such  a  kind  that 
when  the  two  subjects  are  so  collocated  as  to  act  upon 
each  other,  a  result  similar  to  that  produced  in  the 
first  case  will  be  produced  in  the  second  also  ?  If 
the  properties  of  this  arsenic  are  different  from  those 
of  the  other,  or  if  the  second  animal,  though  looking 
like  the  first,  has  a  different  internal  constitution, 
there  is  no  reason  why  death  should  result.  (Cf.  Mill, 
Logic,  Bk.  iii.  ch.  xxii.  sect.  2.)  This  sort  of  uni- 
formity— an  uniformity  primarily  of  co-existence — it 
is  which  .we  look  for,  and  of  which  we  constantly  dis- 
cover fresh  cases,  these  enabling  us  to  predict  that  if 
Subjects  having  certain  characteristics  are  collocated, 
certain  changes  in  them  will  take  place.  Laws  of 
Succession  in  events  seem  thus  to  depend  upon  laws 
of  Go-existence  of  characteristics  in  Subjects.  On  the 
other  hand,  Ave  cannot  predict  new  collocations  of 
Subjects  of  Attributes. 

It  seems,  further,  that  not  only  is  every  charac- 
teristic invariably  accompanied  by  a  certain  other 
characteristic,  as  Bacon  surmised,  but  also  that  every 
kind  of  characteristic  is  one  of  an  unique  group  with 
which  it  is  invariably  and  insej)arably  connected.  We 
certainly  act  as  if  we  believed  this ;  from  the  percep- 
tion of  a  mere  odour,  we  infer  unhesitatingly  the  neigh- 
bourhood of  roses,  or  jessamine,  or  lavender,  of  coffee 
or  tea,  hay,  ripening  corn,  freshly  fallen  snow,  or  a 
beanfield;  from  a  mere  vocal  sound,  we  infer  the 
neighbourhood  of  a  man  or  woman,  or  child,  or  bird. 


■*''''''°'*'^****^*iTfiiini<«miiitiiiii«^  ***■'•"  miiifiii  iinirimrtliiiilif'iiniiiM 


138 


INDUCTIONS. 


dog or  even  a  particular  individual  in  a  particular 

mood.     A  mere  touch  or  taste  will  enable  us  fully 
to  describe  objects  of  a  familiar  kind ;  the  mere  view 
of  a  thing  will  enable  us  to  say  what  it  is  called,  what 
other  characteristics  it  possesses,  how  it  will  behave 
under  a  great  variety  of  circumstances.     For  instance, 
if  I  see  an  object  looking  like  a  squirrel,  sitting  on  the 
top  bar  of  a  stile,  or  on  a  branch,  I  unhesitatingly  say 
that  it  is  called  a  squirrel,  and  infer  that  if  I  startle 
it,  it  will  escape  with  the  kind  of  movement  common 
to  squirrels ;  that  if  I  shoot  it  and  examine  its  struc- 
ture, I  shall  find  it  to  have  a  backbone,  a  brain,  etc. 
No  two  things  are  alike  only  in  visual  appearance  or 
only  in  smell,  or  only  in  taste,  and  so  on.     From  one 
bone  a  whole  skeleton  may  be  made  out ;  from  one 
specially  modified  symptom  the  whole  diagnosis  of  a 

disease. 

In  all  these  cases  we  proceed  by  the  rule  that  if 
anything,  X,  is  like  another  thing,  Y,  in  one  respect, 
it  is  like  it  in  a  plurahty  of  respects.  But  the  admis- 
sion of  this  rule,  and  of  the  Principle  of  Interdepend- 
ence which  it  involves,  is  not  all  that  is   necessary 

before  any  practical  application  of  them   can  be 

made,  we  not  only  need  to  know  that  similar  pheno- 
mena have  similar  interdependents,  but  also  to  know, 
what,  in  any  given  case,  those  interdependents  are. 

How  are  we  to  proceed  in  determining  this  in  any 
case  ?  For  instance,  on  what  grounds  should  we  justify 
our  beUef  that  fragrance  of  a  particular   character 


INDUCTIONS. 


139 


is  inseparable  from  the  various  qualities  of  form, 
colour,  etc.,  characteristic  of  white  violets  (QWV),  that 
equality  of  angles  at  the  base  is  interdependent  with 
equality  of  sides  in  a  triangle,  that  capacity  of  destroy- 
ing animal  life  is  inseparable  from  the  qualities  of 
taste,  colour,  specific  gravity,  and  so  on,  which  we 
regard  as  characteristic  of  arsenic  ? 

I  think  we  should  say  that  we  believe  in  this  inter- 
dependence in  the  case  of  the  fragrance,  because 
wherever  we  have  recognised  the  fragrance,  we  have 
found  that  violets  were  present — it  has  not  occurred 
in  company  with  roses,  geraniums,  daisies,  mignonette, 
and  so  on.  All  cases  of  the  fragrance  have  agreed  in 
occurring  in  connection  with  the  presence  of  violets. 
On  the  strength  of  this  Agreement,  we  conclude  (by 
the  Method  of  Agreement)  that  there  is  interde- 
pendence between  the  fragrance,  and  the  various 
characteristic  attributes  of  form,  colour,  etc.,  by 
which  we  recognise  white  violets. 

If  we  add  to  the  above  reason  the  further  considera- 
tion that  we  have  never  met  with  fresh  white  violets 
unaccompanied  by  the  fragrance  in  question,  then  we 
further  strengthen  our  conclusion  as  to  the  inter- 
dependence of  the  odour  and  the  other  attributes, 
finding  that  not  only  is  the  presence  of  the  odour 
accompanied  by  the  presence  of  the  other  qualities, 
but  also  the  absence  of  the  odour  is  accompanied  by 
the  absence  of  the  other  qualities.  Hence  we  con- 
clude by  what  is  called  the  Method  of  Agreement  in 


140 


INDUCTIONS. 


Presence  and  Absence,  or  the  Joint  Method  of  Agree- 
ment and  Difference. 

The  Arguments  may  be  formulated  thus — 

Method  of  Agreement : 

If  in  my  experience  F  has  always  been  accom- 
panied by  QWV,  then  F  is  inseparable  from 
QWV;  F  has  been  so  accompanied;  .*.  F  is 
inseparable  from  QWV,  and  all  cases  of  F  are 
cases  of  QWV. 
Method  of  Agreement  in  Presence  and  Absence : 

If,  in  my  experience,  the  presence  of  F  has  always 
been  accompanied  by  the  presence  of  QWV,  and 
the  absence  of  F  has  always  been  accompanied 
by  the  absence  of  QWV,  then  F  and  QWV  are 
inseparable;  the  presence  and  absence  of  F 
have  been  so  accompanied ;  .  * .  F  and  QWV 
are  inseparable. 

And  F  and  QWV  being  inseparable,  it  of  course 
follows  that  all  cases  of  F  are  cases  of  QWV, 
and  all  cases  of  QWV  are  cases  of  F. 
(This  latter  argument  might  also  be  expressed  as 
follows : — 

If  F  does  not  occur  without  QWV,  and  QWV 
does  not  occur  without  F,  then  F  and  QWV 
are  inseparable,  etc.) 

Here  we  conclude  inseparability  from  several 
observations  of  concurrent  presence  and  concurrent 
absence :  our  conclusion  is  based  on  the  principle  that 


INDUCTIONS. 


141 


characteristics  which,  whenever  they  are  met  with,  are 
met  with  together,  must  be  inseparable  co-existents. 
We  do  not  perceive  any  intrinsic  connection  between 
the  form,  growth,  and  so  on,  of  the  flower  and  the 
accompanying  fragrance. 

But  it  is  different  in  the  case  of  the  connection 
between  Equality  of  Sides  in  a  triangle  and  Equality 
of  the  Angles  at  the  Base.  Here  the  interdependence 
of  ES  and  EAB  is  a  matter  of  direct  perception — 
having  gone  through  the  proof  in  a  single  case,  the  in- 
separability is  apparent  beyond  the  possibility  of  doubt 
^we  see  that  if  the  sides  are  equal  the  angles  must 
be  equal,  and  if  the  angles  are  equal  the  sides  must 
be  equal.  It  is  because  of  this  actual  perception  of 
inseparability,  that  one  instance  is  always  sufficient 
in  the  case  of  Mathematical  Inductions,  that  we  do 
not  use  the  Inductive  Methods  in  establishing  them, 
and  that  Mathematical  generalisations  are  regarded 
as  having  a  certainty  that  is  unquestionable  and 
unique.  The  inseparability  is  obvious  and  self-evi- 
dent, instead  of  being  assumed  (as  in  the  case  of 
the  violets),  in  order  to  account  for  repeated  cases  of 
co-existence. 

In  the  case  of  any  deadly  poison,  such  as  arsenic, 
our  conclusion  that  the  qualities  (of  taste,  colour, 
specific  gravity,  and  so  on)  which  we  regard  as  char- 
acteristic of  arsenic  are  inseparable  from  poisonous- 
ness,  has  probably  been  reached  by  the  help  of  what 
is  called    the   Method   of   Difference.      We   observe 


wAftiffiBaitfit'iflniiiinrfiiiArnti^ 


142 


INDUCTIONS. 


that  the  mtroduction  into  an  animal  system  of  the 
substance  having  the  characteristic  quahties  of  taste, 
etc.,  referred  to,  is  followed  by  speedy  death,  and  we 
arsfue  as  follows : — 

If  the  introduction  of  A  was  followed  by  D,  A  is  in- 
separable from  D  ;  The  introduction  of  A  was  followed 
by  D,  therefore  A  is  inseparable  from  D. 

It  is,  of  course,  understood  that  the  introduction  of 
A  was  the  only  thing  that  happened  to  which  it  would 
be  possible  to  attribute  D.  A  single  careful  experi- 
ment by  the  Method  of  Difference  is  considered 
sufficient  to  prove  interdependence.  If  a  dose  of  some 
new  substance  to  a  healthy  animal  were  followed  by 
immediate  convulsions  ending  in  death,  no  one  would 
doubt  the  poisonous  quality  of  the  substance.  Or,  to 
take  a  very  homely  example — if  I  put  a  lump  of  sugar 
into  a  cup  containing  coffee  and  milk,  and  on  tasting 
the  mixture  find  that  it  has  a  sweetness  which  it  had 
not  before  the  introduction  of  the  sugar,  I  feel  per- 
fectly sure  that  with  the  quaUties  of  colour,  weight, 
etc.,  which  were  apparent  in  what  I  called  the  lump 
of  sugar,  there  was  connected  the  capacity  of  sweeten- 
ing a  liquid  in  which  it  was  dissolved — in  other  words, 
I  know  that  the  dissolution  of  the  sugar  in  the  coffee 
is  what  has  caused  its  sweetness. 

Or  suppose  that  my  fire  is  smoking  furiously,  and  I 
shut  the  window,  which  was  open,  and  immediately 
the  smoking  ceases,  I  conclude  that  the  open  window 
was  [part]  cause  of  the  smoking.     Or  if  I  am  wearing 


INDUCTIONS. 


148 


blue  spectacles  and  everything  looks  blue,  and  then  I 
put  on  green  spectacles  and  nothing  looks  blue,  I 
conclude  that  it  was  the  blueness  of  the  spectacles 
which  made  everything  look  blue  to  me. 

The  Method  called  the  Method  of  Residues  is  a 
form  of  the  Method  of  Difference.  It  is  extremely 
valuable,  and  is  constantly  used  both  in  the  most 
everyday  matters  and  also  in  scientific  investigations. 
For  instance,  if  I  fill  a  large  jar  with  honey,  having 
previously  weighed  the  jar,  then  the  simplest  mode  of 
ascertaining  the  weight  of  the  honey  is  to  weigh  the 
whole,  and  subtract  the  weight  of  the  empty  jar. 
Supposing  that  the  jar  empty  weighed  2  lbs.,  and  that 
with  the  honey  in  it  weighs  12  lbs.  Then  from  12  I 
subtract  2,  and  conclude  that  the  honey  weighs  10 
lbs.     The  case  may  be  represented  as  follows : 

(Jar  +  Honey)       is        (2  lbs.  -}- 10  lbs.  in  weight) 
(Jar)      ...       is         (2  lbs.) 
.  • .  (Honey)  is  .     .       (10  lbs.) 

(Jar)  and  (2  lbs.)  being  subtracted  (Honey)  and 
(10  lbs.)  remain  as  a  Residue. 

I  know  that  there  is  nothing  in  the  scales  but  the 
Jar  and  the  Honey.  I  know  that  together  these 
weigh  12  lbs.  I  also  know  that  the  Jar  alone  weighs 
2  lbs.  Therefore  the  Residue  on  the  one  side,  namely 
10  lbs.,  must  belong  to  the  Residue  on  the  other  side, 
namely  the  Honey — the  introduction  of  the  Honey 
has  caused  an  increase  of  10  lbs.  in  weisfht.  I 
know  henceforward  that  inseparable  from  the  other 


144 


INDUCTIONS. 


attributes  of  my  Jar  is  a  capacity  of  holding  10  lbs.  of 
Honey — that  inseparable  from  the  other  attributes 
of  that  10  lbs.  of  Honey  is  the  capacity  to  fill  my  Jar 
(or  any  vessel  of  the  same  dimensions). 

What  is  called  the  Method  of  Concomitant  Varia- 
tions is  also  a  mode  of  the  Method  of  Difference.  In 
this  Method,  as  its  name  implies,  interdependence 
between  any  two  phenomena  is  inferred  from  the  fact 
that  the  amount  of  the  one  varies  with  the  amount  of 
the  other.  If  I  find  that  two  lumps  of  sugar  make 
my  tea  sweeter  than  one,  and  that  the  introduction 
of  a  third  makes  it  sweeter  still,  I  have  a  proof,  by 
the  Method  of  Concomitant  Variations,  of  the  sweet- 
ening quality  of  sugar  in  that  instance.  Or  if  I  find 
that  the  barometer  falls  as  the  weather  gets  worse, 
and  rises  as  the  weather  improves,  I  infer  interde- 
pendence between  the  state  of  the  weather  and  the 
height  of  the  barometer,  in  the  cases  observed. 

We  may  perhaps  sum  up  as  follows  the  postulates 
upon  which  these  Methods  {cf.  Index,  Mill's  Methods 
of  Experimeiital  Inquiry)  proceed  : — 

If  A  has  never  been  found  without  B  (nor  B  without 
A) ;  or  if  the  introduction  of  A  is  followed  by  B,  or 
the  removal  of  A  by  the  disappearance  of  B;  or  if 
variation  of  the  quantity  of  A  is  accompanied  or 
followed  by  variation  in  the  quantity  of  B ;  or  if  in 
any  clearly  marked-off  set  of  attributes  or  events 
(AC-BE)  C  and  E  are  interdependent — then  A  and 
B  are  interdependent. 


INDUCTIONS. 


145 


For  the  sake  of  illustration  the  reasoning  involved 
in  the  inductive  generalisation  about  Arsenic  may 
here  be  stated  in  full : — 

If  the  introduction  of  one  phenomenon  (e.g. 
Arsenic)  is  followed  by  a  second  phenomenon 
(e.g.  Death),  then  the  two  phenomena  are  inter- 
dependent ; 

The  introduction  of  Arsenic  was  on  a  given  oc- 
casion followed  by  Death ; 

.  • .  Arsenic  and  Death  were  on  a  given  occasion 
interdependent. 

Here  (having  first  of  all  assumed  that  any  phenom- 
enon in  any  given  case  is  inseparable  from  sorae  other 
phenomena)  we  prove  by  the  Method  of  Difference, 
that  two  given  phenomena  [namely  administration  of 
Arsenic  and  Death]  are  [on  a  given  occasion]  insepar- 
able [because  the  introduction  of  A  has  been  followed 
by  D].  The  interdependent  phenomena  in  question 
not  being  co-existent  but  antecedent  and  consequent, 
they  are  related  as  Cause  and  Effect.  Therefore  we 
go  on 

If  Arsenic  was  on  one  occasion  Cause  of  Death, 

Arsenic  will  be  always  Cause  of  Death ; 
Arsenic  was  on  one  occasion  Cause  of  death ; 

Arsenic  will  be  always  Cause  of  Death — 

that  is 

All  Arsenic  is  a  Cause  of  Death. 

K 


146 


INDUCTIONS. 


Here  we  prove  the  general  law  from  the  special  case 
by  help  of  the  principle  of  Uniformity  in  Causation. 

In  an  Inductive  argument  by  Analogy,  the  inter- 
dependence that  we  rely  upon  is  inferred  from  the 
complexity  or  amount  of  interdependence  already 
known  or  supposed.  For  instance,  if  we  know  that 
two  objects,  X  and  Y,  are  aUke  in  having  a  large 
number  of  interdependent  attributes — say  (A,B,C,D,E) 
—and  X  is  found  to  have  the  further  attribute  F,  we 
conclude  that  F  is  interdependent  with  the  group 
(A,B,C,D,E)— and  therefore  that  Y  is  also  F.  There 
is  a  considerable  presumption  that  if  a  large  group  of 
attributes  occur  in  more  than  one  individual,  those 
attributes  are  inseparable— and  if,  in  any  object,  a 
large  number  of  its  attributes  are  inseparable,  there 
is  a  considerable  presumption  that  any  other  attribute 
of  it  will  be  inseparable  also.  In  Analogy  we  argue 
explicitly  from  Particular  to  Particular,  but  iimplicitly 
from  Particular  to  Universal. 

If  a  botanist  in  exploring  a  new  region  meets  a 
flower  which  is  new  to  him,  and  which  has  very  dis- 
tinctive form  and  colouring,  and  also  on  a  near 
approach  is  found  to  have  a  very  pecuUar  fragrance : 
and  then  he  observes  another  flow^er  precisely  similar 
to  the  first  in  form  and  colour— he  will  have  reason  to 
expect  that  the  second  flower  will  have  an  odour  like 
the  first.  In  doing  this  he  is  making  an  inference  by 
Analogy.  His  thought  is:  The  second  flower  resembles 
the  first  in  form,  colour,  size,  and  so  on— therefore  the 


INDUCTIONS. 


147 


form,  colour,  size,  and  other  visible  attributes  com- 
mon to  the  two  flowers  are  interdependent— therefore 
probably  the  further  attribute  observed  in  the  first 
flower  was  interdependent  with  the  numerous  visible 
attributes— and  if  the  several  attributes  were  inter- 
dependent in  the  first  case,  they  will  be  interdepen- 
dent also  in  the  second— (and  therefore  in  all). 

The  Principle  of  Interdependence  involves  the 
axiom  that  No  two  things  are  alike  in  one  respect 
only.  To.  this  we  may  add  that  No  thing  mlunlike 
another  in  one  respect  only  :  nor  does  a  thmg^change 
in  one  respect  only.— If  we  observe  two  things  to  be 
unhke  in  one  respect,  we  always  infer  further  unlike- 
ness ;  if  we  observe  a  person  or  thing  to  be  changed 
in  one  point,  we  always  infer  further  change.  Two 
axioms  complementary  to  these  are,  that  No  two 
things  are  alike  in  all  respects;  and  that  No  two 
things  are  unlike  in  all  respects. 

The  maxim  by  which  we  are  guided  in  practice 
might  perhaps  be  said  to  be  this,  Apparent  likeness, 
unlikeness,  or  alteration  is  accompanied  by  non- 
apparent  likeness,  unlikeness,  or  alteration. 

In  an  Inductive  Generalisation  there  is  a  character- 
istic element  which  essentially  diflerentiates  it  from 
all  the  other  Kelations  of  Propositions  with  which 
Logic  deals,  namely,  an  element  of  Discovery— since 
the  very  condition  of  Induction  is  perception  or 
recognition  of  the  Universal  in  the  Particular.  In 
Induction  there  seem  to  be  three  aspects  or  stages. 


I  i 


148 


INDUCTIONS. 


First,    a    perception    of   connection   (co-existent    or 
sequent)  between  phenomena  in  some  particular  case 
or  cases.      Second,  a  proof  that  the  connection   in 
that  case  or  cases  is  one  of  interdependence.     Third, 
an  extension  from  the  known  case  to  the  unknown 
cases— a  recognition  that  the  particular  interdepend- 
ence involves  a  connection  holding  universally.     In 
Mill's  treatment  of  Inductions,  the  first  aspect,  and  in 
Whewell's,  the  third  aspect,  are  comparatively  in  the 
background.     The  first  stage  is  the  sphere  of  Hypo- 
thesis.    It  is  clear  that  this  must  both  chronologi- 
cally and  logically  come  first.    Before  interdependence 
between  A  and  B  can  be  proved  or  even  investigated, 
A  and  B  uuist  have  been  thought  of  as  connected,  the 
notion  or  Hypothesis  of  A's  being  Concomitant  of  B,  or 
Cause  of  B,  must  have  occurred  to  some  one's  mind. 

The  Hypothesis  may  be  simple  or  complex,  easy  or 
difficult,  but  in  every  case  of  Induction  it  is  the 
indispensable  starting-point. 

The  business  of  Logic,  at  this  juncture,  is  to  require 
the  fulfilment  of  certain  conditions  on  the  part  of  any 
Hypothesis  before  it  is  regarded  as  admissible.  These 
conditions  appear  to  be,  first,  that  the  Hypothesis 
should  be  in  harmony  with  other  knowledge ;  second, 
that  it  should  (at  least  partially)  explain  and  connect 
the  facts  to  which  it  is  appUed. 

The  remaining  business  of  Logic  in  Induction  is,  to 
jmtify  (a)  the  Hypothesis  and  (b)  its  extension  from 
known  to  unknown  cases. 


INDUCTIONS. 


149 


I  have  already  spoken,  in  this  Section,  of  the  assump- 
tions, and  the  connections  of  Propositions  which  seem 
to  be  required  for  such  justification.  But  the  assump- 
tions themselves  (the  Principle  of  Interdependence, 
etc.)  perhaps  need  justification.  The  justification 
might  be  offered,  that  these  very  assumptions  are 
necessarily  involved  in  all  inductions — inductions 
which  we  constantly  make,  and  on  the  trustworthi- 
ness of  which  we  unhesitatingly  depend.  If  we  accept 
the  inductions  we  must  in  consistency  accept  the 
principles  which  they  involve.  And  if  we  do  not 
accept  the  inductions,  we  are  entangled  in  a  web  of 
hopeless  inconsistency.  And  in  a  later  Section 
(Section  xix.)  we  shall  see  the  extent  to  which  the 
Principle  of  Induction  is  on  the  same  footing  as  the 
Principle  which  expresses  the  condition  of  significant 
categorical  assertion. 


ft 


INFERENTIAL  MEDIATE  INFERENCES. 


151 


SECTION    XIV. 

INFERENTIAL   MEDIATE   INFERENCES. 

An  Inferential  Mediate  Inference  (or  Argument)  is 
a  Mediate  Inference  consisting  of  Inferential  Proposi- 
tions, or  of  Inferential  and  Categorical  Propositions. 

Inferential  Arguments  are  of  two  kinds,  namely  (I.) 
Pure ;  (II.)  Mixed. 

(I.)  A  Pure  Inferential  Argument  is  an  Argument  of 
which  the  Conclusion  and  both  Premisses  are  Inferen- 
tial. 

(II.)  A  Mixed  Inferential  Argument  is  an  Argument 
of  which  the  Major  Premiss  is  Inferential,  the  Minor 
Premiss  and  the  Conclusion  being  Categorical. 

Pure  Inferentials  may  be  divided  into  (1)  Hypo- 
theticals  and  (2)  Conditionals;  Mixed  Inferentials  into 
(3)  Hypothetico-Categoricals,  and  (4)  Conditio-Cate- 
goricals. 

The  following  may  be  suggested  as  Canons  of  (1), 
(2),  (3),  (4)  respectively : — 

(1)  If  from  one  Proposition,  A,  another  Proposition, 
C,  is  inferrible ;  and  from  C  there  is  inferrible  a  third 
Proposition,  D :  then  D  is  inferrible  from  A,  and  not- A 
from  not-D.^ 

1  A  valid  Inferential  Argument  may  need  to  have  some  of  its 
Propositions  obvertcd  before  this  Canon  will  apply  directly. 
150 


(2)  If  from  the  presence  of  a  distinctive  mark,  D,  in 
any  member  of  a  class,  K,  a  second  mark,  M,  may  be 
inferred ;  and  if  from  the  presence  of  M  in  any  K  the 
presence  of  a  further  mark,  M',  may  be  inferred :  then 
from  the  presence  of  D  in  any  K  the  presence  of  M' 
may  be  inferred,  and  from  the  absence  of  M'  in  any 
K  the  absence  of  D  may  be  inferred.^ 

(3)  If  one  Proposition,  C,  is  inferrible  from  another 
Proposition,  A ;  then  the  assertion  of  A  justifies  the 
assertion,  of  C,  and  the  denial  of  C  justifies  the  denial 

of  A. 

(4)  If  from  some  distinguishing  mark,  D,  in  any 
member  of  a  given  class,  K,  some  further  mark,  M,  is 
to  be  inferred;  then  the  assertion  that  any  K  is  D 
justifies  the  assertion  that  that  K  is  also  M  ;  and  the 
assertion  that  any  K  is  not  M  justifies  the  further 
assertion  that  that  K  is  also  not  D. 

1  A  valid  Inferential  Argument  may  need  to  have  some  of  its 
Propositions  obverted  before  this  Canon  will  apply  directly. 


m 


152 


INFERENTIAL  MEDIATE  INFERENCES. 


X 
< 


o 

H 


Si 


C3» 
O 

I 


s 

s 


P         .^' 


o 


CO 

O 

Co 


43 

cS 

43 


1^ 


m 


O 

a 

QQ 

•l-H 

Q 


5^ 


>>  &i      CO 

^  .2  Q 


o 

E3 
I 

CO 

Q 

>< 

OQ 
•  >.< 

Q 
X 


o 

a 

■  o 


Zfl     43 


I 


Qj     00 

.2  P^ 

&4 


43 

o 
;3 

■ 

CO 


03 


-2 
•2 


43 
00 


43 


00 


Q  Pm  a 


CO  » 


00 


-»^# 
•<!>» 


t>%    05      t»^    00  43 

§      C55)— I  H- 1 

O  5^ 


30 

5Q 


G  W  - 


OQ      03 


o 


O  <3l   f^ 

^       «     OQ 

QQ      03    " 


SECTION    XY. 

ALTERNATIVE  OR  DISJUNCTIVE  MEDIATE  INFERENCES. 

An  Alternative  Argument  may  be  defined  as 

An  Argument  of  which  one  Premiss  is  an  Alter- 
native Proposition  or  a  combination  of  Alter- 
native Propositions ;  and  of  which  one  Premiss 
and  the  Conclusion,  or  both  Premisses,  or  both 
Premisses  and  the  Conclusion,  TYiay  be  Alter- 
native. 
Alternative  Arguments  (or  Mediate  Inferences)  may 
be  divided  into,  (I.)  Pure,  and  (II.)  Mixed. 

(I.)  In  a  Pure  Alternative,  both  of  the  Premisses 
and  the  Conclusion  are  Alternative.    E.g. 
C  is  D  or  A  is  not  B 
E  is  F  or  C  is  not  D 

E  is  F  or  A  is  not  B. 
(II.)  Mixed  Alternatives  may  be  distinguished  as 
(1)  Categorico- Alternative,  in  which  either  constituent 
(Major  or  Minor  Premiss  or  Conclusion)  of  the  Argu- 
ment that  is  not  Alternative  is  Categorical ;  and  (2) 
Inferentio- Alternative,  in  which  the  Major  Premiss  is 
always  inferential  in  form,  and  the  other  Premiss  and 

153 


154 


ALTERNATIVE  OR  DISJUNCTIVE 


the  Conclusion  are  either  (a)  one  Alternative  and  the 
other  Categorical,  or  (h)  both  Alternative. 

Inferentio-Alternative  Syllogisms,  which  include 
what  are  commonly  called  Dilemmas,  may  be  divided 
into  Hypothetico-Alternative  and  Conditio-Alterna- 
tive  ;  and  each  of  these  again  into  Ponend  and 
ToUend  (corresponding  to  the  affirmative  and  negative 
forms  of  Mixed  Inferential  Arguments). 

The  following  may  be  suggested  as  Canons  of 

Pure  Alternatives -.—From  two  Alternative  Pro- 
positions, of  which  one,  and  one  only,  has  an  Alter- 
native that  is  the  negative  of  an  Alternative  in  the 
other  (the  other  Alternatives  being  distinct  from  the 
first  and  from  each  other),  a  third  Alternative  Pro- 
position may  be  inferred,  having  for  its  members  the 
remaining  Alternatives  of  the  Premisses. 

Categorico- Alternatives :— The  denial  of  one  mem- 
ber (or  more)  of  any  Alternation  (or  combination  of 
Alternations)  justifies  the   affirmation  of  the   other 

member  or  members. 

Hypothetico-Alternatives :— Of  two  or  more  Hy- 
pothetical Propositions  connected  by  and,  if  the 
Antecedents  be  alternatively  affirmed,  then  the  Con- 
sequents may  be  affirmed ;  and  if  the  Consequents  be 
alternatively  denied,  then  the  Antecedents  may  be 

denied. 

Conditio-Alternatives :— (i.)  Of  any  two  Conditional 
Propositions  connected  by  avd,  if  the  Predicates 
of  the  Antecedents  are  alternatively  affirmed  of  what 


MEDIATE  INFERENCES. 


155 


is  indicated  by  the  Subject-name  of  the  Antecedents : 
then  the  Predicate  [s]  of  the  Consequent  [s]  may  be 
affirmed  of  the  same. 

(ii.)  Of  any  two  Conditional  Propositions  connected 
by  and,  if  the  Predicates  of  the  Consequents  are 
alternatively  denied  of  what  is  indicated  by  the  Sub- 
ject-name of  the  Antecedents:  then  the  Predicates 
of  the  Antecedents  may  be  denied  of  the  same. 


156 


ALTERNATIVE  MEDIATE  INFERENCES. 


o 
o 

I— ( 

H 
O 

Q 


;> 

H 

< 

H 

< 


00 


00 

o 

CO 


5^ 


-4) 


OQ 
•i-l    to 

I      OQ     OQ 


o 

OQ 


o 

OQ 


y 


<w 


5*  2 


O 


«|^ 
eS         O 

W".2 .2  .2 
.2QPQ 
P  >>.2  2 


^53 


at 

O 


CD 


-  s    kS 

V     ft       CO 


03 


o 


S  2 
"do       o  ^ 

^      1  —  — 


feffi.2  _ 

.2.2W-; 


OQ 


5:  - 


X 


^      "^ 


CO 

<4-l 

3  IIh 


O     00 


•^.2 

o  . 

r  o 


fe  .2  ^  2 


•-^  <i  rK  "-' 


SECTION    XVI. 

DIVISION,  CLASSIFICATION,  AND  SYSTEMATISATION. 

In  the  Sections  on  Immediate  Inferences  and  In- 
compatible Propositions,  we  were  concerned  specially 
with  inferential  relations  between  two  Propositions: 
in  discussing  Mediate  Inferences,  we  dealt  with  the 
inferential  relations  between  two  Propositions  taken 
together  and  a  third;  in  this  Section  we  go  on  to 
consider  the  questions  of  Method  which  come  under 
the  head  of  Classification  and  Systematisation. 

Perhaps  this  is  the  most  convenient  place  for  a 
word  with  reference  to  the  general  arrangements  of 
Propositions  and  Groups  of  Propositions,  with  a  view 
to  the  communication  or  recording  of  knowledge.  In 
this  case,  as  in  the  case  of  Definitions,  the  rules  which 
we  can  lay  do^vn  are  not  in  themselves  sufficient  to 
secure  good  results,  though  they  go  some  way  towards 
it,  and  the  breach  of  them  certainly  entails  bad  results. 
We  may  say  briefly  that,  in  any  Discourse  or  Treatise, 
the  end  which  that  Discourse  or  Treatise  is  intended 
to  subserve  should  be  steadily  kept  in  view;  that 
tautologies,   obscurities,    inconsistencies,    and   irrele- 

157 


}^J;i^:.^;K;=  «y  ,:;i:  *:>|r'|.^  ■:  :;"t  ^; 


158    DIVISION,  CLASSIFICATION,  AND  SYSTEM ATISATION. 

vancies  should  be  avoided ;  that  the  relations  of  the 
parts  of  the  subject  should  be  plainly  set  forth; 
and  that  it  is  desirable  that  Propositions  which  are 
accepted  as  fundamental  should  be  themselves  self- 
evident,  or  inferences  from  other  Propositions  which 
are  self-evident.  (We  cannot,  of  course,  start  originally 
from  statements  which  require  proof :  if  we  professed 
to  do  this,  it  would  be  the  statements  given  in  proof 
that  we  should  really  start  from ;  we  have  to  begin 
with  something  that  is  incapable  of  proof,  and  can  be 
accepted  without  proof) 

The  further  conditions  of  a  satisfactory  choice  and 
articulation  of  material  are  to  be  found  in  acuteness, 
sagacity,  ingenuity,  industry,  trained  skill,  and  other 
intellectual  and  moral  qualities  which  enable  their 
possessors  to  make  right  selections  and  happy  guesses 
in  cases  where  rules  are  either  useless  or  not  forth- 
coming. 

Classification,  which  is  bound  up  with  Division, 
should  be  distinguished  from  Glassing,  which  has  a 
close  connection  with  Detinition.  Classing  consists  in' 
grouping  together  a  number  of  numerically  distinct 
individuals  in  virtue  of  their  possession  of  similar 
attributes,  these  attributes  being  those  which  are 
unfolded  in  the  definition  of  the  class-name. 

In  Classification,  we  are  concerned  with  the  relations 
of  a  number  of  classes,  the  objects  composing  those 
classes  being  regarded  as  members  of  a  system  of 
individuals.     These  relations  may  be  expressed  in  a 


DIVISION,  CLASSIFICATION,  AND  SYSTEM  ATISATION.    159 

series  of  Relative  Propositions — (e.g.  Triangles  /are/ 
divided  into  Equilateral,  Isosceles,  and  Scalene,  etc.) 
— but  they  are  frequently  and  conveniently  expressed 
in  Tables.  A  Table  of  Family  Relationships,  for 
instance,  presents  clearly  and  in  brief  compass  a 
multitude  of  relationships  between  persons  which 
could  only  be  conveyed  with  tediousness  and  much 
risk  of  confusion  by  Propositions  alone,  without  the 
aid  of  Tables.  The  help  which  these  give  is  similar  to 
that  afforded  by  maps,  or  by  diagrammatic  represen- 
tation. 

In  all  cases,  the  function  of  a  classification  or 
systematisation,  however  presented,  is  to  facilitate 
comprehension  of  the  relations  of  objects  to  one 
another,  to  bring  out  the  Unity  in  Difference  which 
belongs  to  any  group  of  related  things. 

I  observed,  just  above,  that  Classification  is  bound 
up  with  Division — it  may  indeed  be  said  that  Division 
and  Classification  are  the  same  thing  looked  at  from 
different  points  of  view ;  any  table  presenting  a  Divi- 
sion, presents  also  a  Classification.  A  Division  starts 
with  unity  and  differentiates  it ;  a  Classification  starts 
with  multiplicity,  and  reduces  it  to  unity,  or  at  leasi 
to  order.  If  the  Classification  stops  short  of  unity,  it 
presents  not  one  Division,  but  a  plurality  of  Divisions. 
A  Table  is  generally  most  convenient  which  starts 
from  unity — that  is,  which  is  primarily  a  Division. 
Some  tables  in  Whewell's  Novum  Organon  Renova- 
tum  are  an  example  of  the  reverse  arrangement,  which 


160    DIVISION,  CLASSIFICATION,  AND  SYSTEMATISATION. 

is  that  which  naturally  occurs  in  a  synthetic  pro- 
cedure ;  while  Division  is  as  naturally  the  appropriate 
form    in    cases   where    the    procedure    is    primarily 

analytical. 

From  a  Division  or  Classification,  a  brief  Definition 
of  any  Constituent  class,  except  the  Summum  Genus  or 
widest  class,  may  be  framed,  by  taking  the  Proximate 
Genus  of  that  Constituent  class,  and  adding  to  it  the 
Differentia— that  is,  the  characteristics  by  which  the 
particular  sub-class  is  marked  off*  from  the  rest  of  the 
Genus.  Take,  e/j.,  '  Fig.  1,'  in  the  subjoined  Table- 
Inferences 


Immediate 


Mediate 


Inductive 


Deductive 


Syllogistic  Argument 


Relative  Argument 


Categorical  Syll.     Inferential  Syll.     Alternative  Syll 


Fig.  1.     Fig.  2.     Fig.  3.     Fig.  4. 

'Fig.  1'  may  be  defined  by  giving  the  Proximate 
Genus  (or  next  class  above  it),  and  adding  to  this  the 
characteristics  by  which  it  is  distinguished  from  Fig. 
2,  Fig.  3,  and  Fig.  4,  thus— 

'Fig.   1   is  a  Categorical  Syllogism  in  which   the 


DIVISION,  CLASSIFICATION,  AND  SYSTEMATISATION.    161 

Middle  Term  is  Subject  in  the  Major  Premiss,  and 
Predicate  in  the  Minor  Premiss.' 

A  good  Division  or  Classification  should  be  appro- 
priate to  the  purpose  in  hand;  co-ordinate  classes 
should  never  overlap ;  and  at  every  stage  of  a  Division 
or  Classification,  the  co-ordinate  classes  should  be 
identical  in  appUcation  or  extension  with  the  co- 
ordinate classes  of  every  other  stage,  and  with  the 
Summum  Genus.     E.g.  in  the  following  Division  or 

Classification — 

Triangles  (1) 


Equilateral  (2) 
Equiangular  (5) 


Isosceles  (3) 


Scalene  (4) 


Right- Angled  (7) 
Acute- Angled  (6)     Obtuse- Angled  (8) 


Acute -Angled  (9) 


Obtuse- Angled  (11) 


Right- Angled  (10) 

the  co-ordinate  classes  (2)  (3)  (4)  do  not  overlap,  nor 
do  the  co-ordinate  classes  (5)  (6)  (7)  (8)  (9)  (10)  (11); 
the  co-ordinate  classes  (2)  (3)  (4)  are  identical  in 
extension  with  (5)  (6)  (7)  (8)  (9)  (10)  (11),  and  each  of 
these  two  groups  of  classes  is  identical  in  extension 
with  the  Summum  Genus  (1)— that  is,  they  contain 
the  very  same  objects. 

If  the  name  Glassing  is  assigned  to  (a)  the  collec- 
tion into  groups  of  objects  which  are  qualitatively 

L 


T'  ^S^^i"?^;=^:^'S^|i^?;!^^Fis?^^*;w^^  'iTWP^?'^^.^-  "^  'rv- JSr'^^-" 


162    DIVISION,  CLASSIFICATION,  AND  SYSTEM ATISATION. 

similar,  but  numerically  distinct,  and  Classification 
to  (b)  the  arrangement  of  such  groups  in  their 
relations  to  one  another,  there  still  remains  to  be 
named  and  considered  a  third  arrangement,  namely 
(c)  that  of  diftering  parts  of  a  whole  (whether  single 
objects  or  groups  of  objects)  in  their  relations  to  each 
other,  and  to  the  whole.  This  may  perhaps  be  dis- 
tinguished from  ((()  and  (h)  as  Systematisatioi}.  This 
term  seems  more  applicable  than  Classification  to,  e.fj., 
the  arrangement  of  the  Sciences  in  relation  to  one 
another,  or  the  arrangement  of  the  parts  of  an 
organic  whole  such  as  the  human  body,  of  genealogical 
relationships,  of  the  subdivisions  of  any  such  quan- 
titative whole  as,  e.g.,  a  ton,  a  square  mile — and  so  on. 
It  may  be  observed  that  a  Systematisation  may 
often  include  Classification.  For  instance,  the  body 
of  Logical  Science  itself,  which  must  be  regarded  as 
a  Systematisation,  includes  various  Classifications — 
such  as  the  Classification  of  Terms  or  Propositions. 
Again,  in  Morphology,  which  is  a  systematising  rather 
than  a  classificatory  Science,  various  Classifications 
are  included. 


SECTION    XVII. 

DEFINITION  AND  LANGUAGE. 

By  the  Definition  of  any  word  is  meant  a  statement 
of  the  meaning  or  signification  of  the  word — that  is, 
a  statement  of  the  characteristics  on  account  of  which 
the  name  is  applied,  and  in  the  absence  of  any  of 
which  it  would  not  be  applied.  We  may  take  the 
view  that  every  name  is  capable  of  being  defined,  if 
we  include  the  characteristic  of  being  called  by  the 
name  among  those  characteristics  of  the  thing  which 
are  comprised  in  the  signification  of  its  name. 
(There  is,  of  course,  no  question  that  the  name 
by  which  anything  is  called  is  a  characteristic, 
and  to  us  a  very  important  characteristic,  of  it.) 
On  this  view  even  so-called  Proper  Names  would 
have  a  Definition,  but  it  would  be  a  Definition 
giving  only  a  minimum  of  information  about  the 
things  called  by  the  name ;  for  of  any  object  known 
to  us  merely  by  a  Proper  Name,  we  can  only  predicate 
(1)  what  is  common  to  all  Subjects  of  Attributes,  (2) 
unique  individuality,  (3)  a  distinctive  name,  (4)  what 
that  name  is.  Take,  for  instance,  any  appellation 
which,  from  the  circumstances  of  its  use,  the  mode  in 

163 


■Iff  tfiiiffriiiriffiiit  iitiTrif 


'Mfa^^'*'**-^^*^ 


164 


DEFINITION  AND  LANGUAGE. 


which  it  is  written,  or  for  any  other  reason,  I  know  to 
be  a  Proper  Name— 6.^.  Richmond.     I  can  certainly 
affirm  that  any  object  to  which  this  word  applies  (in 
its  capacity  of  Proper  Name),  has  the  characteristics 
common   to  all  Subjects  of  Attributes,  has  unique 
individuality  and   a   distinctive   appellation,  namely 
Richmond.     And   for   some   purposes— e.r/.  statistics 
respecting  the  relative  frequency  of  occurrence  of  cer- 
tain names — the  grouping  of  individuals  in  accordance 
with  their  names  may  be  interesting  and  useful,  just 
as  the  alphabetical  grouping  of  words  in  a  Dictionary 
or  Index   may  be  useful  for  reference.     Still   such 
classings  are,  from  most  points  of  view,  highly  artificial 
—that  is,  they  do  not  seem  to  be  strongly  suggested 
by  the  things  themselves  which  are  classed  (as,  for 
instance,  the   division   of  animals  into   quadrupeds, 
birds,  lishes,  reptiles,  and  insects  is  suggested)— and 
for  the  general  purposes  of  life,  what  a  man's  Proper 
Name  is,  is  insignificant ;  what  concerns  himself  and 
others  is,  that  he  should  be  known  by  some  name  or 
other.     Hence,  notwithstanding  that  it  is  possible  to 
give  a  vague  Definition  to  Proper  Names,  the  Defini- 
tion is  not  of  much  use.     It  does  not  serve  for  recog- 
nition in  fresh  cases;  and  a  knowledge  of  the  application 
in  one  case  does  not  help  us  to  a  knowledge  of  the 
application  in  other  cases.    But  with  Attribute  Names, 
Adjectives,  and  Common  Names  (e.g.  Triangularity, 
Red,  Fern),  with  any  combination  of  these  (e.g.  A 
large  oak-tree),  and  with  any  mixed  name  (e.g.  Tom 


DEFINITION  AND  LANGUAGE. 


165 


Smith's  brother),  in  as  far  as  it  consists  of  Attribute 
Names,  Adjectives,  or  Common  Names,  it  is  the  case 
either  that  Definition  may  serve  for  recognition,  or 
that  knowledge  of  appUcation  in  one  case  helps  us  to 
knowledge  of  application  in  other  cases. 

With    regard    to    such   fundamentally    important 
words  as  White,  Cold,  Visible,  Tangible,  Liquid,  Pain, 
Pleasure,  and  so  on  (cf.  Mill,  Logic,  i.  155,  9th  ed.),  it 
is  necessary,  in  order  to  understand  and  apply  the 
words,  that  one  should  have  had  experience  of  the 
things  indicated,  and  also  definite  information  in  some 
given  case,  of  the  applicability  of  the  name  to  the  thing. 
Unless  I  have  felt,  I  can  attach  no  vahd  meaning  to 
any  word  which  indicates  Sensation ;  unless  I  have 
seen  colours,  I  can  attach  no  valid  meaning  to  any 
words  which  indicate  the  colours.  Red,  Blue,  etc. :  and 
unless  in  some  individual  case  in  my  experience  the 
names  (or  names  which  I  know  to  be  their  equiva- 
lents) have  been  assigned  to  the  things,  I  can  never 
know  the  application  of  the  names.     And  similarly 
with    such   words    as   Quixotism,  Johnsonese,  Aris- 
totelian ;  they  cannot  be  understood  or  defined  with- 
out  individual  acquaintance  with   the  character  or 
works  of  the  personages  referred  to. 

I  said  above, '  these  names,  or  names  which  I  know 
to  he  their  equivalents;  because,  of  course,  when  I  have 
once  learned  to  attach  some  name  to  a  thing,  I  can  by 
means  of  that  name  learn  all  the  other  names  of  the 
thing.    (It  is  obviously,  to  a  large  extent,  by  such  means 


166 


DEFINITION  AND  LANGUAGE. 


that  fresh  languages  are  learnt.)  For  instance,  if  I 
have  learnt  the  application  of  the  word  Pain,  I  need  only 
to  be  told  that  Suffering,  Schnierz,  Leiden,  Doideiir, 
and  so  on,  have  an  identical  application,  in  order  to 
understand  those  words  when  I  hear  them.  In  the  case 
of  certain  other  words — such  as  Trilateral ity  Octagon 
— Definition  may  be  a  guide  to  application,  without  any 
previous  knowledge  of  the  application  of  the  word. 
For  instance,  if  I  know  what  is  meant  by  Eight,  by 
Side,  and  by  Figure,  I  may  be  able  to  recognise  an 
Octagon,  and  call  it  by  its  name  the  first  time  I  see 
one.  But  it  may  be  admitted  that,  in  the  case  of  most 
things,  mere  Definition  alone  is  not  the  most  satis- 
factory guide  to  identifying  things  in  the  first  instance 
— and  that  unless  we  had  actually  met  with  triangles 
and  circles,  roses  and  fritillaries,  castles  and  cathedrals, 
oaks  and  beeches,  horses  and  dogs,  lions  and  elephants, 
and  so  on,  the  names  of  those  objects,  however  care- 
fully defined,  would  convey  but  little  meaning  to  us, 
and  our  thoughts  about  the  objects  themselves  would 
inevitably  be  far  more  vague  and  faulty  than  they  are 
at  present.  The  construction  of  any  Definition  is,  of 
course,  necessarily  subsequent  to  acquaintance  with 
the  thing  defined  (or  its  elements). 

With  Proper  Names  alone,  of  all  Names,  it  is  ab- 
solutely indispensable  to  have  the  application  of  the 
name  pointed  out  in  the  case  of  every  individual 
person  or  thing — the  objects  which  have  Proper 
Names  interest  us  as  individuals  and  not  as  mere 


DEFINITION  AND  LANGUAGE. 


167 


members  of  classes.     No  doubt  if  it  were  possible  to 
bestow  upon  individuals  convenient  names  significant 
of  all  their  qualities— past,  present,  and  to  come— 
such  names  would  take  the  place  of  '  Proper '  Names. 
But  such  names  are  obviously  impossible,  both  because 
there  never  is  such  knowledge  of  individuals,  and  also 
because,  if  there  were,  names  conveying  the  knowledge 
would  be  quite  unadapted  for  use.     What  is  indis- 
pensable, and  at  the  same  time  possible,  in  the  case  of 
persons  or  things  distinguished  by  Proper  Names,  is 
to  attach  to  them  names  which  indicate  definitely  and 
easily  which  of  certain  known  individuals  it  is  that  in 
any  given  case  is  being  referred  to ;  and  this  function 
is  fulfilled  by  Proper  Names. 

There  are  certain  Names  composed  entirely  of 
Attribute  Names,  Adjectives,  or  Common  Names,  and 
having  a  maximum  of  Signification,  which  have 
necessarily,  or  actually,  an  unique  Application— e.^. 
The  longest  river  in  the  world,  The  noblest  friendship 
of  antiquity.  And  in  the  case  of  such  Adjectives  as 
Shakespearian,  Rembrandtesque,  which  are  potentially 
general,  it  is  quite  possible  that  there  may  never  exist 
anything  to  which  those  terms  can  be  applied  except 
the  productions  of  Shakespeare  and  Rembrandt  re- 
spectively. But  the  majority  of  Adjectives  and  of 
Attribute  and  Common  Names  have  an  application 
both  actually  and  potentially  general;  and  it  is  of 
such  words  that  Definitions  are  ordinarily  most  useful. 
In  these  cases— that  is,  where  we  are  concerned  with 


wm 


168 


DEFINITION  AND  LANGUAGE. 


classes,  and  connections  of  characteristics — Definitions 
may  both  furnish  guidance  in  appHcation,  and  also 
help  to  bring  to  mind  the  characteristics  of  the  things 
we  are  referring  to. 

Certain  rules  for  the  framing  of  Definitions  are 
commonly  provided  in  logical  handbooks,  of  which  it 
may  be  said  that  though  a  Definition  which  conforms 
to  them  may  be  bad,  a  Definition  which  does  not  con- 
form is  certainly  not  good.  These  rules  are  to  the 
effect  that  a  Definition  must  not  be  tautological,  that 
it  should  be  expressed  in  clear  and  simple  and  (pre- 
ferably) affirmative  terms,  that  the  word  defined  and 
the  Definition  of  it  must  have  identical  application, 
that  the  Definition  must  state  the  Attributes  included 
in  the  Signification,  and  those  only.  It  may  be  added 
that  it  is  generally  desirable  that  a  Definition  should 
be  brief;  hence  the  old  rule  that  a  Definition  (of  any 
Class  Name)  should  be  by  Proximate  Genus,  and 
Differentia  is  a  useful  one.  When  we  define  Man  as 
Rational  Animal  or  Triangle  as  Plane  figure  enclosed 
hy  three  straight  lines,  we  are  defining  by  Proximate 
Genus  and  Differentia.  These  definitions  are  both 
economical  and  adequate,  because  the  terms  Animal, 
Plane  Figure  are  so  significant;  and  they  are 
obviously  in  accordance  with  the  other  rules  given 
above. 

Some  of  the  most  important  Definitions  are  of  Class- 
Names  ;  and,  as  remarked  in  the  previous  Section, 
Classing  has  a  close  connection  with  Definition — for 


DEFINITION  AND  LANGUAGE. 


169 


while  Classing  consists  in  grouping  together  a  number 
of  numerically  distinct  things  in  virtue  of  their  pos- 
sessing similar  characteristics,  those  characteristics 
constitute  the  Signification  which  is  unfolded  in  the 
Definition.  And  the  connection  between  Classing 
and  Definition  on  the  one  hand,  and  Induction  on  the 
other,  is  also  very  intimate.  For  it  may  perhaps  be 
said  that  the  majority  of  Class-names  are  a  result  of 
Induction,  and  may  be  unfolded  into  a  statement  of 
the  interdependence,  or  inseparable  and  uniform  co- 
existence, of  attributes— since  it  is  by  a  combination 
of  attributes,  and  not  by  merely  one  attribute  or 
kind  of  attribute,  that  we  know  the  objects  called  by 
those  Class-names.  Consider,  for  instance,  such  names 
as  Violet,  Oak,  Squirrel,  Water,  Air,  Circle.  From  our 
knowledge  of  the  application  and  meaning  of  the  word 
Circle,  we  may  extract,  e.g.,  the  proposition  that  any 
closed  plane  figure  having  every  point  of  the  circum- 
ference equidistant  from  a  point  within  it,  is  a  figure 
of  which  the  diameters  are  equal.  Similarly  from  a 
knowledge  of  the  meaning  and  application  of  any  of 
the  other  names  instanced,  we  may  frame  Universal 
Propositions  which  assert  a  co-existence  of  character- 
istics.—And  every  fresh  Induction  that  is  summed  up 
in  the  Signification  of  a  Class-name  is,  of  course, 
expressed  in  the  Definition  of  the  name. 

It  is  easy  to  define  Definition  by  saying  that  it 
consists  in  giving  the  Signification  of  Names;  but 
we   require   to  know  further  by   what   criterion   to 


170 


DEFINITION  AND  LANGUAGE. 


decide  which  characteristics  of  a  thing  should  be  in- 
chided  in  the  Signification,  and  the  settlement  of 
the  Signification  is  the  most  difficult  and  important 
point  in  defining.  A  Definition  may  give  a  Proxi- 
mate Genus  and  Difference ;  it  may  be  clear,  simple, 
affirmative,  and  not  tautological.  Definition,  and  word 
defined  may  be  exactly  equivalent;  but  owing  to  a 
mistaken  choice  of  Signification,  it  may  be  a  very 
bad  Definition.  For  instance,  the  Definitions  of 
Man  as  A  featherless  biped,  or  A  bartering  animal, 
break  no  rules,  and  yet  for  ordinary  purposes  are 
absurd  Definitions.  Perhaps  the  only  useful  general 
rules  that  can  be  given  for  the  choice  of  Significa- 
tion are  the  following: — (1)  The  Signification  ought 
to  be  as  far  as  possible  conformable  to  usage — 
as  regards  non-technical  words,  ordinary  usage,  and 
the  authorities  generally  recognised  (that  is,  current 
speech  and  writing,  standard  authors  and  accepted 
dictionaries);  in  the  case  of  terms  which  are  technical 
or  quasi-technical  (Slang,  Scientific  Terms,  Provincial- 
isms, etc.),  the  usage  of  those  recognised  as  the  most 
competent  judges.  (It  is  in  an  analogous  way  that 
we  come  to  know — in  as  far  as  we  do  know — who  are 
the  best  lawyers,  physicians,  orators,  artists,  and  so 
on.)  Signification  ought  to  be  (2)  consistent ;  (3)  ap- 
propriate to  the  purpose  in  hand — {cf.  Sidgwick, 
Principles  of  Political  Economy,  bk.  i.  ch.  ii.  p.  54, 
1st  ed.) ; — also  (4)  the  characteristics  comprised  in  the 
Signification   should  be,  if  possible,  impressive  and 


DEFINITION  AND  LANGUAGE. 


171 


distinctive.  In  all  cases,  of  course,  limits  are  set  to 
the  variations  of  the  Definition  of  any  word  by  its 
Application.  And  with  regard  to  the  great  body  of 
words  in  any  important  language,  their  application 
is  practically  fixed,  and  a  person  who  does  not  know 
what  this  application  is  does  not  know  the  language. 

Since  any  Definition  is  framed  with  some  definite 
end  in  view,  and  every  class  of  objects  has  a  multitude 
of  common  characters,  and  may  be  regarded  from 
different  points  of  view,  every  Class-name  is  susceptible 
of  a  plurality  of  Definitions,  application  remaining  fixed 
— e.g.  Man  may  be  defined  (as  by  Cuvier,  in  order  to 
indicate  his  place  in  a  certain  classification  of  animals) 
as  A  w^ammiferous  animal  having  two  hands;  or 
as  A  rational  animal;  or  An  animal  capable  of 
speech;  or  as  An  animate  creature  responsible  for 
his  actions.    There  is,  however,  even  with  reference  to 
Application  regarded  as  fixed,  often  a  '  ragged  edge  of 
usage' — a  margin  of  inconsistency  which  admissible 
Definition  must  exclude.     In  the  case  of  a  'dead' 
language,  e.g.  Greek,  there  is  complete  fixity.     In  a 
'living'  language  with  a  literature,  though  there  is 
practical  fixity  at  any  given  time,  yet  as  manners  and 
customs  and  life  altogether  change,  and  as  knowledge 
increases,  and  fresh  discoveries,  fresh  analyses,  and 
fresh  syntheses  are  made,  some  old  words  have  to  be 
modified,  and  some  new  words  have  to  be  adopted — it 
is  not  possible  to  confine  the  new  wine  in  the  old 
bottles,  to  keep  a  growing,  changing  body  altogether 


172 


DEFINITION  AND  LANGUAGE. 


within  the  limits  of  a  cut-and-dried  integument. 
The  necessity  of  names  for  new  things  is  obvious — 
one  of  the  first  requisites  of  an  adequate  language  is 
to  have  a  name  wherever  it  is  wanted.  A  language 
that  had  a  sufficiency  of  names  and  other  words,  every 
name  having  its  Application  definite  and  consistent, 
its  Signification  clear  and  known,  no  name  having  two 
applications,  and  no  name  being  the  synonym  of  any 
other,  would  be  an  almost  ideal  instrument  of  record 
and  communication.  In  such  a  language  many 
common  causes  of  error  would  be  absent  —  the 
synonyms  which  are  a  source  of  tautology ;  the  words 
which  are  ambiguous  because  they  have  a  plurality  of 
meanings  (as,  for  instance.  Board,  Nature,  Interest), 
or  a  doubtful  meaning  (as,  e.g.,  Beauty,  Natural,  Luxu- 
rious), and  give  rise  to  confusion  productive  of  fallacy; 
the  dearth  of  appropriate  terms,  which  necessitates 
the  use  of  some  roundabout  awkward  phrase,  or  some 
old  word  in  a  new  sense  (thus  increasing  ambiguity), 
or  some  new  word  which  has  the  disadvantages  of 
strangeness. 

In  the  case,  especially,  of  ambiguous  words,  the 
force  which  they  have  when  used  in  assertion  often 
depends  greatly  upon  their  context ;  and  not  only  the 
verbal  context,  but  also  the  unspoken  context  of 
circumstances — including  even  such  circumstances  as 
position  on  a  page,  kind  of  type,  etc.  The  degree  of 
dependence  varies:  in  the  case  of  words  with  more 
than   one    Application,    the   Application    cannot    be 


DEFINITION  AND  LANGUAGE. 


173 


guessed  at  without  reference  to  context.  But  in  such 
cases,  Application  being  determined,  Definition  may 
be  easy.  Again,  where  general  Application  is  not 
doubtful,  shades  of  meaning  may  be  largely  deter- 
mined by  context.  The  Application  of  Proper  Names 
seems  to  be  entirely  determined  by  context. 

And  where  neither  Application  nor  Definition  would 
be  held  to  be  disputable,  that  unique,  individual  con- 
text which  a  word  has  in  the  mind  of  each  person 
who  uses  it  is  often  very  important,  and  may  be  very 
misleading — the  force  and  effect  of  a  word  or  a  phrase 
being   largely   determined    by  the   associations    and 
suggestions  it  brings  with  it.     We  find  in  this  con- 
sideration a  key  to  many  controversies — among  others, 
to  the  question  in  dispute  between  Mill  and  Jevons  as 
to  the  force  of  Proper  Names.     Mill  regards  them  as 
unmeaning,  as  conveying  no  information  respecting 
the  persons  to  whom  they  apply ;  while,  on  the  other 
hand,  Jevons  regards  them  as  giving  more  information 
than  any  other  kind  of  name.     The  ground  of  dispute 
vanishes  when  we  realise  that  what  Jevons  is  thinking 
of  is,  the  associations  and  suggestions  called  up  by  the 
name  of  a  person  whom  one  knows  as  an  individual : 
he  observes  that,  'Any  proper   name,  such  as  John 
Smith,  is  almost  without  meaning  until   we  know 
the  John  Smith  in  question ' ;  and  he  would  be  quite 
ready  to  admit  that,  prior  to  personal  acquaintance,  a 
Proper  Name  can  give  no  guidance  whatever  as  to  its 
own  application,  since  John  Smith  '  certainly  does  not 


174 


DEFINITION  AND  LANGUAGE. 


bear  his  name  written  upon  his  brow.'  Mill,  on  the 
other  hand,  is  thinking  of  the  amount  of  information 
which  Proper  Names  are  capable  of  conveying  con- 
cerning an  individual,  apart  from  special  associations 
and  personal  acquaintance. 

Again,  often,  as  a  matter  of  practice,  one  person 
in  using  a  word  may  be  thinking  of  one  part  of  the 
attributes  and  another  person  of  another — although 
they  would  agree  in  admitting  the  same  application 
of  the  word.  For  instance,  suppose  '  The  Country '  is 
given  as  an  essay  subject  to  a  class,  one  essayist  in 
writing  may  be  thinking  of  a  west-country  farm  in 
sunnner-time ;  another  may  be  thinking  of  the  sea- 
side or  of  moors  in  autumn ;  a  third  may  have  in 
mind  a  windy  hillside  residence  in  winter.  Or  sup- 
pose that  in  a  Logic  Examination  Paper  a  question  is 
asked  about '  Induction,'  one  candidate  in  answering 
may  be  thinking  only  of  the  element  of  Discovery 
which  is  distinctive  of  Induction ;  another  may  have 
his  attention  fixed  upon  the  Methods  of  Proof  by 
which  Inductive  Discovery  is  established.  Or  (a  very 
common  case)  while  one  person  is  thinking  of  some 
particular  instance  or  instances,  another  is  referring 
to  a  different  instance — both  perhaps  being  right  in 
the  Application  of  the  name,  but  one  or  both  possibly 
referring  to  Attributes  special  to  the  individual  case 
and  not  common  to  the  Class.  For  instance,  two 
children  of  different  families,  in  using  the  names 
Home  or  Father,  may  each  unintentionally  be  credit- 


DEFINITION  AND  LANGUAGE. 


175 


ing  a  whole  class  with  a  combination  of  Attributes 
more  or  less  unique,  more  or  less  special  to  his  own 
particular  circumstances — and  the  case  of  the  one  may 
differ  to  any  extent  from  that  of  the  other.  Probably 
it  is  Technical  Names— such  as  Polypodium,  Scarlet 
Fever,  Predicable,  Oxygen— which  are  least  subject 
to  ambiguity,  whether  of  Application  or  Signification. 
Without  appealing  to  context — even  regarding  them 
detached  from  assertion  (as  in  the  columns  of  a 
dictionary),  we  feel  Httle  doubt  about  their  meaning. 

Experiment  seems  to  show  that  the  'mental 
equivalents'  which  actually  occur  to  people's  minds 
in  using  names  differ  quite  extraordinarily  in  different 
cases.  Take  such  a  word  as  Animal,  for  instance. 
The  idea  corresponding  to  the  word  must  be  in 
some  respects  similar  in  the  minds  of  all  those  who 
understand  its  AppHcation  and  Signification.  But  in 
addition  to  this  common  element,  it  will  call  up  in 
one  person's  mind  the  name  simply  printed,  or  written 
in  a  particular  handwriting,  or  printed  on  the  outside 
of  a  particular  book ;  or  it  may  call  up  the  image  of 
a  *  picture  alphabet'  with  illustrations  of  animals, 
or  some  story  of  animal  intelligence,  or  a  pet  animal, 
or  the  first  animal  one  cared  for,  or  the  cat  of  the 
house,  or  an  idea  of  the  movements  made  in  speaking 
the  word,  or  some  striking  delineation  of  an  animal 
seen  in  a  magic-lantern  exhibition  or  a  picture 
gallery,  or  Noah's  ark,  or  a  mere  shapeless  moving 
mass.      If  one  dwells  upon   the  word,  an  immense 


■.jatoftMBJiw 


.JL.*.MM..^IH,f  Wllfclir 


'litiiiiirtafllnflmMitffliil'tifilWiAiyrrMiiiiil^ 


176  DEFINITION  AND  LANGUAGE. 

succession  of  ideas  may  occur  to  one ;  in  rapid  reading 
or  speaking,  perhaps  only  one  or  two.     What  seems 
very  often  to  happen  in  the  latter  case  is,  that  one 
just  thinks  very  transiently  of  the  word  itself,  with 
a  satisfactory,  though   evanescent,   consciousness  of 
understanding  its  meaning  and   apphcation.  ^   If  m 
reading  or  listening  one  meets  a  word  of  which  one 
does  not  know  the  meaning,  one  is  instantly  arrested 
by  a  feeling  of  dissatisfaction,  due  to  the  recognition 
of  a  hindrance  to  comprehension.     As  an  illustration 
of  what  I  mean,  I  may  refer  to  what  happens  when, 
in  looking  rapidly  through  a  passage  in  some  toler- 
ably familiar  language  with  a  view  to  translating  it, 
one  comes  here  and  there  upon  words  of  which  one 
does  not  know  the   meaning.      The   translator,  the 
moment  he  sees  the  other  words,  and  without  any 
pause  to  realise  their  full  hnport,  is  aware  that  he 
knows  their  signification ;  and  he  is  aware,  just  as 
instantaneously,  that  he  does  not  know  the  meaning 

of  the  strange  words. 

What  perhaps  happens  often  to  some  people,  m 
connection  with  Conunon  and  Proper  Names,  is  that 
these  call  up  in  the  mind  a  kind  of '  generic  image.' 
E.g.  the  word  horse  may  suggest  a  sort  of  vague 
image,  like  a  horse  seen  at  a  little  distance  in  a  fog. 
which  is  definite  enough  not  to  be  mistaken  lor  any 
other  creature,  but  not  definite  enough  to  be  identified 
as  of  this  or  that  breed,  colour,  size,  etc.,  much  less  as 
a  definite  individual ;  quadruped  may  suggest  merely 


DEFINITION  AND  LANGUAGE. 


177 


four  vague  elementary  legs,  supporting  an  elementary 
body,  like  a  child's  drawing — and  so  on.  Our  image 
of  many  acquaintances,  and  even  friends,  may  be  very 
vague — just  definite  enough  to  enable  us  to  know 
them  when  we  see  them,  but  by  no  means  definite 
enough  to  enable  us  to  accurately  draw  or  describe 
them,  or  perhaps  even  to  say  by  what  sign  or  signs 
we  recognise  them. 

Butler  (Sermon  i.,  note  2)  puts  the  case  of  a  man 
whom  he  supposes  to  'go  through  some  laborious 
work,  upon  promise  of  a  great  reward,  without  any 
distinct  knowledge  what  the  reward  would  be.'  The 
state  of  this  man's  mind  with  reference  to  the  re- 
ward must,  I  imagine,  correspond  in  essentials  with 
the  state  of  mind  of  a  person  dwelling  on  a  Common 
Name  withdrawn  from  context ;  but  of  course  names 
ordinarily  occur  to  us  with  a  context  which  helps  to 
determine  their  mental  equivalent.^ 

^  In  this  and  some  other  Sections  1  have  taken  passages  from  my 
Elements  of  Logic. 


M 


SECTION    XVIII. 

FALLACIES. 

Confusion  is  often  a  source  of  Fallacy,  but  it  can- 
not be  said  that  Confusion  is  Fallacy,  because  in  as 
far  as  there  is  confusion,  it  is  doubtful  what  our  pro- 
positions really  are  or  mean.     This  confusion  may  be 
(«)  because  of  the  ambiguity  of  some  Term  or  Term- 
constituent  (Term-name  or  Term-indicator).     Fallacy 
produced  by  the  use  of  Question-begging  Epithets 
seems  to  come  under  this  head.     For  instance,  the 
words  business-like,  orthodox,  inartistic,  un-English, 
are  often  used  in  a  question-begging  way ;  the  reason 
being   that  besides    the   actual   signification   of  the 
names,  they  carry  a  vague  implication  of  praise  or 
blame,  and  upon  this  implication  there  may  be  based 
an  explicit  condemnation  or  approbation  which  the 
term  itself  either  does  not  justify  in  any  way  at  all, 
or  only  justifies  in  a  circular  and  tautological  fashion 
—thus  '  begging  the  question.'     Again  (6)  confusion 
may  be  due  to  ambiguity  of  construction.     Or  (c)  to 
ambiguity  of  context  or  implication.     What  is  called 
the  Fallacy  of  Continuous  Questioning  may  be  refer- 

178 


FALLACIES. 


179 


rible  to  confusion  of  this  third  sort.  E.g.  if  I  ask, 
'  Is  what  you  are  thinking  of  over  1  lb.  in  weight  ? ' 
the  difficulty  to  the  person  questioned  of  framing  an 
answer,  if  his  '  object '  is  without  weight,  is  due  to 
what  may  be  called  ambiguity  of  implication  or 
reference,  for  there  is  no  ambiguity  in  the  terms  or 
construction  of  my  question.  'Why  does  a  dead  fish 
weigh  more  than  a  living  one  ? '  is  another  and 
familiar  instance  of  a  fallacious  question.  In  these 
cases  it  appears  to  be  assumed  that  the  conditions 
exist  which  are  necessary  in  order  to  make  the  ques- 
tion such  as  is  capable  of  receiving  a  valid  answer, 
without  involving  an  answer  to  some  other  question 
as  well — when,  as  a  matter  of  fact,  this  may  not  be  so. 
In  other  cases  of  Fallacious  Questioning,  the  fallacy 
(in  as  far  as  there  is  fallacy)  may  be  due  to  ambiguity 
of  construction;  e.g.  Are  you  ready  and  willing? 
Have  you  read  Robert  Elsniere  and  Joh7i  Ward, 
Preacher  ?     Are  Billy  and  Colin  at  school  ? 

Fallacies  of  Equivocation  are  Fallacies  due  to  am- 
biguity of  Terms ;  Fallacies  of  Amphibology  are  due  to 
ambiguity  of  Construction.  The  Fallacies  of  Composi- 
tion (concluding  of  the  whole  what  has  been  asserted 
of  constituents).  Division  (concluding  of  part  what  has 
only  been  asserted  of  the  whole).  Accident  (arguing  from 
a  general  rule  to  a  special  case — A  dicto  sirripliciter 
ad  dictum  secundum  quid),  the  Converse  Fallacy  of 
Accident  (arguing  from  a  special  case  to  a  general 
rule — A  dicto  secundum  quid  ad  dictum  simpliciter), 


180 


FALLACIES. 


and  the  Fallacy  of  arguing  from  one  special  case  to 
another  special  case,  are  all  Fallacies  of  Equivocation. 
When  the  confusion  to  which  such  Fallacies  are  due 
has  been  pointed  out,  they  generally  appear  at  once 
as  Eductive  Fallacies  of  Redundant  Terms,  or  as  Syl- 
logistic Fallacies  of  Redundant  Terms. 

"  If  a  person  were  to  argue  that  his  ailment  is  a  cold, 
and  that  all  cold  is  dispelled  by  heat,  therefore  his 
cold  will  be  dispelled  by  heat,"  he  would  fall  into  a 
simple  Fallacy  of  Equivocation — cold  being  taken  in 
two  different  meanings.  "  Members  of  trades-unions 
often  fall  into"  a  Fallacy  of  Composition.  "They 
argue  that  stone-masons,  by  limiting  the  number  of 
apprentices,  may  raise  their  own  wages;  carpenters 
can  do  the  like;  and  also  brickmakers,  engineers, 
cotton-spinners,  and  so  on  through  the  whole  list  of 
trades.  It  is  quite  true  that  any  one  trade  may  do  so 
to  a  certain  extent;  but  it  does  not  follow  that  all 
trades  taken  together  can  do  it,  because  each  trade,  in 
thus  raising  its  own  wages,  tends  to  injure  the  others 
in  some  degree."  Again,  "  we  sometimes  fall  into  the 
opposite  fallacy  to  that  last  described,  and  argue  that, 
because  something  is  true  of  the  whole  of  a  group  of 
things,  therefore  it  is  true  of  any  of  those  things.  .  .  . 
All  the  soldiers  in  a  regiment  may  be  able  to  capture 
a  town,  but  it  is  absurd  to  suppose  that  therefore 
every  soldier  in  the  regiment  could  capture  the  town 
single-handed."  {Cf.  Jevons,  Primer  of  Logic,  pp. 
114,  117,  118.)     This  is  the  Fallacy  of  Division.     To 


FALLACIES. 


181 


argue  that  because  whoever  intentionally  kills  another 
ought  to  suffer  death,  therefore  a  soldier  who  kills  an 
enemy  in  battle  ought  to  suffer  death,  is  to  fall  into 
the  Fallacy  of  Accident.  To  argue  that  because  alms- 
giving in  certain  cases  is  productive  of  harm,  therefore 
no  aid  should  ever,  under  any  circumstances,  be  given 
to  persons  in  pecuniary  distress,  is  to  commit  the 
Converse  Fallacy  of  Accident.  In  all  these  cases  we 
find  that  we  have  no  true  Middle  Term,  because  the 
ostensible  Middle  Term  is  really  not  the  same  in  the 
two  Premisses. 

Again,  the  Fallacy  commonly  called  Fon-Sequittir 
sometimes  reduces  to  a  Fallacy  of  Redundant  Terms 
(1)  in  the  Premisses  (which  reduces  to  a  case  of  no 
true  Middle  Term),  (2)  in  Premisses  and  Conclusion. 
E.g. 

(2)  The  sea  was  the  place  where  the  incidents  of 
my  story  occurred ; 
There  is  the  sea ; 


Therefore  my  story  is  true. 

Here  the  Terms  of  the  Conclusion  are  not  the 
Major  and  Minor  Terms  of  the  Premisses. 

The  Fallacy  of  the  False  Cause  (A  non  Causa  'pro 
Causa,  Post  hoc  ergo  propter  hoc)  reduces  to  an 
Eductive  Fallacy  of  Redundant  Terms  ('  Simple  Con- 
version of  an  A  Proposition ').     E.g. — 

Whatever  is  cause  of  X  precedes  X ; 
.  • .  Whatever  precedes  X  is  cause  of  X. 


182 


FALLACIES. 


"  I  walk  under  a  ladder  and  lose  the  train  just  after- 
wards. Foolishly  I  attribute  my  misfortune,  not  to 
my  unpunctuality,  but  to  the  ill-luck  resulting  from 
going  under  a  ladder.  A  ship  sails  on  a  Friday  and 
is  shipwrecked,  and  one  of  the  passengers  blames  his 
folly  in  starting  on  an  unlucky  day."  (K.  F.  Clarke, 
Logic,  p.  454.) 

The  Fallacy  of  Irrelevant  Conclusion  is  reducible  to 
an  Eductive  Fallacy  of  Discontinuity  {cf.  post,  p.  185). 
E.g.  a  person  who,  wishing  to  prove  that  S  is  Q,  argues 
as  follows — 

M  is  P 
SisM 

>SisP 

and  offers  this  argument  in  support  of  the  assertion 
S  is  Q,  commits  the  Fallacy  of  Irrelevant  Conclusion 
(Ignoratio  Elenchi).  He  proves  a  Conclusion  other 
than  that  required  to  be  proved.  What  is  implied  in 
this  procedure  is,  that  because  S  is  P,  therefore  S  is  Q. 
When  thus  barely  stated,  the  illicit  nature  of  the 
inference  is  at  once  apparent.  To  such  a  case  the 
rules  of  Eduction  in  Section  x.  will  not  apply.  For 
further  illustration,  take  the  cases  of  the  persons  in 
Punch  who  proved  that  they  (1)  were  not  Toxopholites, 
and  (2)  did  belong  to  the  Psychical  Society,  by  show- 
ing (1)  that  they  belonged  to  the  Church  of  England, 
(2)  that  they  had  been  practising  on  their  brothers' 
bicycles. 


FALLACIES. 


183 


The  Fallacy  known  as  Argunientum  ad  populam, 
comes  under  the  head  of  Ignoratio  Elenchi.  "  The  skil- 
ful barrister  will  often  seek  to  draw  off  the  attention  of 
the  jury  from  the  real  point  at  issue,  viz.  the  guilt  or 
innocence  of  the  prisoner,  by  a  pathetic  description  of 
the  havoc  that  will  be  wrought  in  his  home  if  he  is 
convicted,  or  by  seeking  to  create  an  unfair  prejudice 
against  prosecutor  or  witnesses."     (Clarke,  Logic,  p. 

448.) 

Since  Fallacy  consists  in  either  identifying  what  is 
different,  or  differencing  what  is  identical,  we  get  a 
primary  subdivision  of  Fallacies  into  (a)  those  of 
professed  Difference,  which  may  be  called  Fallacies 
of  Tautology;  {h)  those  of  professed  Identification, 
which  may  be  called  Fallacies  of  Discontinuity. 
{a)  Embraces  all  such  Fallacies  as  Circidits  in 
Definiendo,  Petitio  Principii,  Arguing  in  a  circle. 

Fallacy  in  the  broadest  sense  may  perhaps  be 
defined  as— The  assertion  or  assumption  of  some 
relation  between  (1)  Terms,  or  (2)  Propositions,  which 
does  not  hold  between  them.  (1)  are  not  generally 
treated  among  logical  Fallacies,  though  they  are 
included  by  Mansel  (Mansel's  Aldrich,  Note  M)  as 
Fallacies  of  Judgment.  It  would  be  convenient  to 
call  them  Elemental  Fallacies.  All  combinations  of 
words  which  (i.)  cannot  be  significant,  or  (ii.)  cannot  be 
true,  would  come  under  this  head.  A  is  A  would  be 
a  case  where  compatibility  between  the  Terms  merges 
into  complete  Tautology.     Circular  Definitions  would 


iMiminiiiiiMiiiiiiii>iiin((iliiirnlri[iiiit^  i  - 


184 


FALLACIES. 


also  come  under  this  head — e.g.  Genus  is  the  material 
part  of  Species  (Species  being  a  subdivision  of  Genus) ; 
Sortie  means  not-none  {none  being  in  turn  defined 
as  meaning  not-some),  A  is  not-A  would  be  a  case 
of  (ii.) — the  case  where  diversity  merges  into  absolute 
incompatibility  (or  discontinuity). 

Taking  Fallacy  in  this  wide  sense,  it  appears  that 
breaches  of  the  common  rules  of  Definition,  Division, 
and  Classification  generally,  are  included.  E.g.  in 
Circular  Definitions  and  Cross  Divisions,  we  have 
Tautology ;  breaches  of  the  rule  that  the  sum  of  con- 
stituent Species  is  equal  to  the  Genus,  or  of  the  rule 
that  the  definition  must  be  exactly  equivalent  to  the 
Species  defined,  may  be  exhibited  as  Fallacies  of 
Discontinuity.  But  if  Fallacy  is  understood  in  the 
narrower  sense,  it  may  be  defined  as  follows :— There 
is  Fallacy  whenever  we  conclude  from  one  or  more 
Propositions  to  another,  the  conclusion  not  being 
justified  by  the  premiss  or  premisses. 

This  must  be  understood  to  include  the  cases 
(Tautological)  in  which  a  Proposition,  which  professes 
to  be  a  conclusion,  simply  repeats  the  datum  or  a  part 
of  it,  or  claims  to  be  proved  by  the  help  of  an  assertion 
which  the  professed  conclusion  has  itself  contributed 
to  prove— for  clearly  a  Proposition  can  be  no  justifica- 
tion for  itself. 

Where  fallacious  Inference  is  from  one  proposition 
to  another,  there  is  a  Fallacy  of  Immediate  Inference 
(or  Eduction) ;  where  it  is  from  two  propositions  taken 


FALLACIES. 


185 


together  to  a  third,  there  is  a  Fallacy  of  Mediate 
Inference.  There  are,  besides,  certain  Tautologous 
Fallacies  which  involve  relations  between  a  plurality 
of  Arguments. 


formal  fallacies  of  immediate  inference 

(or  eduction). 

These  may  be  divided  into  Eversive  and  Transver- 
sive  Fallacies.  Eversive  Fallacies  may  be  (I.)  Cate- 
gorical ;  (II.)  Inferential ;  (III.)  Alternative. 

(I.)  Here  we  may  (1)  pass  from  one  proposition  to 
another  when  the  two  propositions  have  no  Term  or 
Term-name  in  common — e.g.  from  M  is  N  to  Q  is  R. 
This  is  not  a  common  form  of  Fallacy.  It  may  be 
called  an  Eductive  Fallacy  of  Four  Term-names.  (2) 
Or  we  may  pass  from  one  proposition  to  a  second 
proposition  which  (a)  contains  one  Term-name  not 
contained  in  the  first  proposition ;  or  (6)  a  Term  having 
a  wider  application  than  the  corresponding  Term  in 
the  first  proposition — e.g.  (a)  All  R  is  Q,  .*.  Some  X  is 
Q ;  (6)  Some  R  is  Q,  .-.  All  R  is  Q  (or  All  Q  is  R). 

(3)  Or  we  may  profess  to  educe  a  proposition  from 
itself — to  infer  S  is  P  from  S  is  P. 

(II.)  Inferential  Fallacies  of  Eduction.  Here,  besides 
Tautological  Fallacies,  in  which  it  is  professed  to 
educe  a  proposition  from  itself,  we  may  instance  two 
Fallacies  of  Discontinuity  which,  from  their  corre- 
spondence with  the  Syllogistic  Inferential  Fallacies, 


186 


FALLACIES. 


might  be  called  the  Fallacy  (a)  of  the  Antecedent, 
(b)  of  the  Consequent. 

^.(/.  (a)IfEisF,  GisH; 

.-.  If  E  is  not  F,  G  is  not  H. 

(h)  If  E  is  F,  G  is  H ; 
.-.  If  G  is  H,  E  is  F. 

(III.)  Alternative  Fallacies  of  Eduction.  Here,  be- 
sides Tautological  Fallacies,  numerous  Fallacies  of 
Discontinuity  are  possible. 

jE7.^.  (1)  AllRisQorT; 
.'.  No  R  is  Q  and  T. 

This  is  a  Fallacy  of  denial. 

(2)  Any  R  is  Q  or  T ; 
.-.  Any  Q  or  T  is  R. 

This  is  a  Fallacy  of  conversion. 

(3)  Some  R  is  Q  or  T ; 
.-.  Any  R  is  Q  or  T. 

This  is  a  Fallacy  of  enlargement. 

(4)  G  is  H  or  E  is  not  F ; 
.-.  G  is  not  H  or  E  is  F. 

This   corresponds   to  the   Inferential   Fallacy  of  the 

Antecedent. 

Transversive  Fallacies  occur  in  passing  from  Cate- 
gorical to  Inferential  or  Alternative  Propositions,  from 
Inferential  to  Categoricals  or  Alternatives,  and  from 


FALLACIES. 


187 


Alternatives    to    Categoricals    or    Inferentials.      All 
Transversive  Fallacies  are  Fallacies  of  Discontinuity. 


FORMAL  FALLACIES  OF  MEDIATE  INFERENCE. 

Syllogistic  (like  Eversive)  Fallacies  fall  into  the 
three  subdivisions  of  (I.)  Categorical;  (II.)  Inferen- 
tial ;  (III.)  Alternative. 

(I.)  In  I.  we  have  either  (i.)  the  case  where  7io  con- 
clusion is  inferrible ;  or  (ii.)  the  case  where  the  pro- 
position, which  is  professedly  inferred,  is  not  inferrible, 
though  sonie  conclusion  is  inferrible — including  the 
case  (tautological)  where  the  proposition  professedly 
inferred  is  simply  a  repetition  of  one  of  the  premisses, 
or  asserts  jpart  of  what  is  asserted  by  one  of  the 
premisses. 

(i.)  All  cases  here  are  reducible  to  cases  (A)  of 
Tautology,  (B)  of  no  true  Middle  Term  in  the  Pre- 
misses, or  (C)  of  Inconsistent  Premisses. 

In  (A)  one  premiss  repeats  the  other,  {a)  wholly,  or 
{h)  partly.     E.g. 


(a)  M  is  P 
MisP 


(6)  All  R  is  Q 
Some  R  is  Q. 


In  (B)  where  there  is  no  true  Middle  Term  in  the 
Premisses,  we  have  (a)  the  case  of  four  Term-names. 
(The  Fallacy  of  Non-Sequitur  may  come  either 
under  this  head  or  under  (ii.)  (/3),  cases  in  which 
the  third  proposition  which  is  inferred  is  not  in- 
ferrible, though  some  conclusion  is  inferrible.)     Then 


188 


FALLACIES. 


(b)  if  the  Term -name  of  the  Middle  Term  is  a 
class-name  qualified  by  Some,  the  So'tne  N  of  one 
premiss  may  be,  for  all  we  know,  quite  different  in 
application  from  the  Some  N  of  the  other  premiss. 
(Some  N  is  ambiguous  on  account  of  the  indeter- 
minateness  of  Some.) 

(c)  If  the  Term-name  of  the  Middle  Term  is 
ambiguous,  again,  for  all  we  know,  it  may  be  a  differ- 
ent Term  in  the  two  premisses. 

And  the  only  case  where  from  two  negative  pre- 
misses it  is  impossible  to  infer  some  conclusion,  is 
the  case  w^here  these  premisses  cannot  be  reduced  to 
affirmative  premisses  having  a  true  Middle  Term — 
that  is,  having  three  Terms,  or  four  Terms,  one  of 
ivh  ich  is  included  in  one  of  the  others.     For  instance, 


NoNisQ     ]       , 

^^    ^  .    ^^      '  reduces  to 

No  R  IS  N     J 


All  X  is  not-Q 
All  N  is  not-R 


and 


No  N  is  Q 
Some  N  is-not  R 


1       ,  f  All  N  is  not-Q 

\  reduces  to  -'j  ^         „  .  ^ 

J  [  bome  X  IS  not-K 


both  formally  justifying  the  conclusion 

Some  not-R  is  not-Q. 
But  from 


Some  N  is  not  Q 
Some  R  is  not  N 


(1) 


no  conclusion  can  be  obtained. 
Again,  from 


\  \ 


FALLACIES. 


189 


Some  N  is  not  Q 
Some  N  is  not  R 


f  (2) 


from 


Some  N  is  not  Q 
Some  N  is  R 


1(3) 


) 


(4) 


and  from 

Some  N  is  Q 
Some  N  is  not  R 

we  can  draw  no  conclusion — because  Some  N  is 
ambiguous,  and  we  do  not  know  that  we  have  a  true 
Middle  Term. 

From  two  (indefinite)  particular  affirmative  pre- 
misses, for  the  same  reason,  we  can  draw  no  con- 
clusion. *  J 

From  a  particular  (indefinite)  Major  and  a  negative 
Minor,  we  can  (indirectly)  get  a  conclusion — e.g. 


Some  N  is  (,) 
No  R  is  N 


}' 


educes  to 


(  Some  N  is  Q 


(  All  N  is  not-R 

which  gives  the  formally  valid  conclusion 

Some  not-R  is  Q. 

And  from  premisses  with  a  negative  Minor  in  Fig.  1, 
we  can  get  a  conclusion  by  reducing  to  Fig.  3.    E.g. 

All  N  is  Q 
No  R  is  N 


} 


reduces  to 


f  All  N  is  Q 
1  AU  N  is  not-R 


and  gives  the  formally  valid  conclusion, 
Some  not-R  is  Q. 


wmem^Ms^seMssMmi^^'^ 


190 


FALLACIES. 


(C)  In  the  case  of  Inconsistent  Premisses  we  may 
have  a  true  Middle  Term,  but  the  extremes  are  the 
negatives  of  each  other.     E.g.  P  is  M,  M  is  not-P. 

(ii.)  Here  we  have  cases  in  which  the  third  proposi- 
tion professedly  inferred  is  not  inferrible,  though  some 
other  proposition  is  inferrible. 

Under  this  head  come  the  Fallacies  of 
(a)  Tautology.     E.<j. — 

M  is  P  \ 

SisM   I  (5) 

M  is  P.  ) 


(^)  Non-Sequitur.     E.(j. — 

All  N  is  Q      \ 

Some  R  is  N   •  (6) 

No  R  is  Q      ) 

(or,  All  X  is  Y,  etc.). 

(In  all  cases  of  (ii.)  except  (a),  the  whole  syllogism 
contains  redundant  Terms — that  is,  it  contains  more 
than  three  Term-names,  or  some  Term  in  the  con- 
clusion is  wider  than  the  corresponding  Term  in  the 
premisses.) 

(7)  Illicit  Major  and  Minor.     E.g. — 

All  N  is  Q      \ 
Some  R  is  n'.  (7j 

All  R  is  Q.     ) 


FALLACIES. 


191 


I 


Some  Q  is  not  N  \ 
AH  R  is  N  I  (8) 

No  R  is  Q.  ) 

(The  conclusion  Some  Q  is  not  R  is  valid.) 
In  these  two  cases  we  conclude  to  a  Term  of  which 
part  (R  minus  Some  R,  Q  minus  Some  Q)  may  be  not 
coincident  with  any  part  of  the  corresponding  Term 
in  the  premisses. 

(3)  Negative  Conclusion  from  Affirmative  Pre- 
misses.    E.g. — 

All  N  is  Q 
All  R  is  N 

No  R  is  Q. 

Again,  we  do  not  know  whether  the  distributed 
Q  of  the  Conclusion  is  wholly  coincident  with  the 
[some]  Q  of  the  Major  Premiss. 

(e)  Affirmative  Conclusion  from  a  Negative  Pre- 
miss.    E.g. — 

No  N  is  Q  \  ( All  N  is  not-Q 

All  R  is  N  V  This  reduces  to  '  All  R  is  N 

AllRisQ.)  (aURIsQ. 

(Four  Term-names.) 

All  the  Categorical  Fallacies  of  Syllogism  pointed 
out  above  are  excluded  by  the  Canon  of  Syllogism  put 
forward  in  Section  xii.  ['  If  the  Application  of  any 
two  Terms  is  identical  (or  distinct),  any  third  Term 
which  has  a  different  Term-name,  and  is  identical  in 


■Biairiift^Mate^rtaate^^ 


192 


FALLACIES. 


Application  with  the  whole  (or  part)  of  one  of  those 
two,  is  also  (in  whole  or  part)  identical  with  the  other 
(or  distinct  from  it),']  For  instance  (1)  and  (2)  are 
incompatible  with  that  part  of  it  which  indicates  that 
there  must  be  Identity  between  two  of  the  Terms. 
For  in  (1)— 

Some  N  is-not  Q 
Some  R  is-not  N — 

if  we  take  either  Q  or  Some  R  as  a  third  Term,  we 
cannot  say  that  it  is  identical  in  application  with  the 
whole  (or   a   part)  of  any  other   Term   in   the  two 

premisses. 

Similar  objections  apply  to  (2)— 

Some  N  is-not  Q 
Some  N  is-not  R. 

And  again,  in  (3),  of  neither  of  the  premisses  can  it  be 
said  that  one  of  its  Terms  is  identical  (in  whole  or 
part)  with  either  Term  of  the  other  premiss,  since 
Some  N  is  ambiguous.     And  the  same  holds  of  (4). 

(5)  is  not  in  accordance  with  the  condition  indicated 
by  the  last  clause  of  the  Canon  (and  referring  to  the 
conclusion),  that '  the  Application  of  any  third  Term 
...  is  also  identical  (or  distinct)  in  whole  or  part, 
with  the  Application  of  the  other '  {i.e.  with  that  other 
which  is  not  a  Middle  Term). 

In  (6),  (7),  (8),  etc.,  a  Term  is  introduced  in  the  con- 
clusion of  which  it  cannot  be  said  that   its  whole 


FALLACIES. 


193 


Syllogisms. 


application  is  either  identical  with,  or  a  part  of,  the 
application  of  any  Term  in  the  premisses. 

11.  Fallacies  of  Inferential  Syllogism. 

These  fall  under  four  heads,  corresponding  to  the 
division  of  Inferential  Syllogisms  into 
(i.)  Pure  Hypothetical 
(ii.)  Pure  Conditional 
(iii.)  Hypothetico-Categorical 
(iv.)  Conditio-Categorical 

Besides  Tautological  Fallacy  which  occurs  under 
each  head,  the  Fallacies  incident  to  (i.)  appear  to  be 
of  two  kinds.  (1)  Where  the  premisses  are  such  that 
no  conclusion  can  be  drawn.  When  this  is  the  case, 
there  is  no  such  connection  between  the  two  premisses 
that  a  third  proposition  (having  elements  in  common 
with  both  premisses)  can  be  inferred  from  them.    E.g. 

IfKisL,  FisG; 

If  D  is  E,  M  is  N : 

If  A  is  B,  C  is  D 
If  C  is  D,  A  is  not  B. 

(2)  Where  the  conclusion  drawn  is  not  deduced  from 
the  premisses,  though  some  other  conclusion  is  de- 
ducible.     E.g. — 

If  K  is  L,  F  is  G : 

IfDisE,  FisnotG: 


If  K  is  not  L,  D  is  E. 


N 


ti.A  A5a^Ma.»a«.«art»a.fl«.Ajj^  ^■...>tt.,..JM.«aBaa 


194 


FALLACIES. 


If  K  is  L,  F  is  G ; 

IfPisE,  FisnotG; 

If  D  is  E,  M  is  P. 
(If  K  is  L,  D  is  not  E  may  be  deduced.) 

IfKisL,  FisG; 
IfFisG,  DisE; 

If  D  is  E,  K  is  L. 
(The   consequence,  If  D  is  not   E,  K    is  not   L,   is 
deducible.) 

(ii.)  Fallacies  of  Pure  Conditional  Syllogism. 
In  as  far  as  Conditional  Propositions  are  similar  to 
Hypotheticals,  the  Fallacies  under  this  head  may  be 
classed  with  those  under  the  preceding  head.  In  as 
far  as  they  are  similar  to  Categoricals,  Conditional 
Fallacies  may  be  classed  as  Categorical. 

(iii.)  and  (iv.)  Fallacies  of  Hypothetico-Categorical 
Syllogism,  and  of  Conditio-Categorical  Syllogism  have 
corresponding  subdivisions.  They  include  Tauto- 
logical Fallacies  and  Fallacies  of  Discontinuity.  The 
chief  Fallacies  of  Discontinuity  are  two— namely  (1) 
the  Fallacy  of  the  Antecedent  (2)  the  Fallacy  of  the 
Consequent.  E.g. 
(1)  If  D  is  E,  F  is  G  ; 

D  is  not  E ;     

F  is  not  G. 

If  any  D  is  E,  that  D  is  F  : 

This  D  is  not  E ;     

This  D  Ts  not  F7~" 


FALLACIES. 


195 


(2)IfDisE,  FisG; 
FisG; 

D  is  E. 

If  any  D  is  E,  that  D  is  F ; 
This  D  is  F ; 

This  D  is  E. 

Fallacy  here  may  be  due  also  (3)  to  the  presence  in 
the  Minor  Premiss  of  a  constituent  not  included  in 
the  Major  Premiss,  thus  rendering  it  impossible  to 
draw  any  conclusion.  And  (4)  it  may  be  due  to  the 
presence  in  the  Conclusion  of  a  constituent  not  con- 
tained in  the  premisses — the  Conclusion  thus  being 
invalid. 

III.  Fallacies  of  Alternative  or  Disjunctive  Syllo- 
(jisnfi. 

In  Pure  Alternative  Syllogisms  we  have  Fallacies 
of  Tautology — 

(1)  In  the  Premisses  alone.     E.g. — 

A  is  B,  or  C  is  D ; 
C  is  D  or  A  is  B. 

(2)  In  concluding  from  valid  premisses  when  {a)  the 
Conclusion  is  the  same  as  a  premiss.     E.g. — 

{a)  A  is  B  or  C  is  D ; 
E  is  F  or  A  is  not  B ; 

A  is  B,  or  C  is  D. 


jjiiiiiirii^^ 


196 


FALLACIES. 


(h)  The  Conclusion  asserts  part  of  a  premiss.     E.g. — 

(b)  C  is  not  D  or  E  is  F ; 
Any  A  is  B  or  C  is  D : 

Some  A  is  B,  or  C  is  J). 

We  may  have  Fallacies  of  Discontinuity — 
(1)  In  the  premisses,  when  the  premisses  are  not 
connected  by  means  of  an  alternative  of  which  the 
affirmative  occurs  in  one  premiss,  and  the  negative  in 
the  other  (the  remaining  alternatives  being  different 
from  one  another).     E.g. — 

A  is  B  or  C  is  D 
E  is  F,  or  G  is  H. 

A  is  B  or  C  is  D 
C  is  D  or  G  is  H. 

A  is  B  or  C  is  D 
A  is  B  or  C  is  not-D. 

(2)  In  passing  from  premisses  to  conclusion,  when  the 
alternatives  of  the  conclusion  are  not  the  extremes  of 
the  premisses.     E.g. — 

C  is  D  or  A  is  not  N 
E  is  F  or  C  is  not  I) 

K  is  H  or  L  is  M. 

The  Fallacies  of  Discontinuity  which  are  most 
obviously  possible  in  what  I  have  called  Categorico- 
Alternative  Syllogisms,  are 

(1)  The  introduction  into  the  Minor  Premiss  of  an 


FALLACIES. 


197 


element  distinct  from  those  contained  in  the  Major 
Premiss — in  which  case  no  inference  is  possible. 

(2)  The  introduction  into  the  Conclusion  of  an 
element  not  contained  in  the  Premisses — in  which 
case  the  Conclusion  is  unjustifiable. 

(3)  The  Fallacies  corresponding  to  the  Inferential 
Fallacies  of  Antecedent  and  Consequent. 

Again,  in  Fallacies  of  Inferentio -Alternative  Syl- 
logism, there  may  be  Fallacy  due  to  the  unwarrantable 
introduction  of  a  fresh  element,  (1)  into  the  Minor 
Premiss,  (2)  into  the  Conclusion;  but  the  chief 
Fallacies  are  those  of  Antecedent  and  Consequent  (as 
in  the  case  of  Inferentio-Categorical  Fallacies).  With 
both  kinds  of  Alternative  Syllogism,  Tautological 
Fallacies  may  occur. 


CIRCULAR  FALLACIES. 

Besides  Elemental,  Eductive,  and  Syllogistic  Fal- 
lacies, there  are  the  Fallacies  that  occur  when,  in  the 
attempt  to  prove  an  assertion,  recourse  is  had  to  some 
proposition  which  that  assertion  itself  has  contributed 
to  prove — which  Fallacies  involve  relations  between  a 
plurality  of  Syllogisms. 

The  name  Circular  Fallacies  may  be  conveniently 
appropriated  to  these.  They  occur  in  the  simplest 
form  when  there  are  only  two  Syllogisms  concerned, 
but  may  (and  often  do)  involve  relations  between 
several  Syllogisms. 


198 


FALLACIES. 


Taking    the    Syl- 


The    following    are    examples, 
logism 

QisP 
MisQ 

MisP 

it  may  be  required  to  prove  M  is  Q.     If  this  is  done 
by  means  of  the  Syllogism 

PisQ 
MisP 

M  is  Q 

Ave  have  a  case  of  circular  reasoning. 

Or  if  we  have  the  Hypothetical  Syllogism 

If  G  is  H,  K  is  L 
If  E  is  F,  G  is  H 

If  E  is  F,  K  is  L 

and  proceed  to  prove  the  Minor  Premiss  by  the  folloAv- 
ing  argument — 

If  K  is  L,  G  is  H 
If  E  is  F,  K  is  L 

If  E  is  F,  G  is  H 

we  have  again  a  case  of  arguing  in  a  circle. 
Again,  taking  the  Syllogism 

If  Jack  is  a  good  boy,  he  will  do  what  he  is  told; 

He  is  a  good  boy ; 

He  will  do  what  he  is  told, 


FALLACIES. 


199 


if  we  go  on  to  prove  the  Minor  Premiss  by  the  follow- 
ing Syllogism — 

If  Jack  will  do  what  he  is  told,  he  is  a  good  boy; 

Jack  will  do  what  he  is  told ; 

He  is  a  good  boy, 
we  have  committed  a  Circular  Fallacy. 


RELATIVE  FALLACIES. 

In  this  Section  we  have,  so  far,  been  concerned  with 
Formal  Fallacies— that  is.  Fallacies  that  may  occur 
in  dealing  with  Absolute  or  Non-relative  Propositions. 
There  are  also,  of  course.  Relative  Fallacies  both  of 
Mediate  and  of  Immediate  Inference— that  is.  Fallacies 
that  can  only  occur  in  dealing  with  Relative  Proposi- 
tions. These,  like  Formal  Fallacies,  may  be  either 
Tautologous  or  Discontinuous ;  and  they  may  all  be 
reduced  to  breaches  either  of  the  Principle  of  Trans- 
formation, or  of  the  Canon  of  Relative  Mediate 
Inferences.     (0/.  pp.  99  and  132.) 


200 


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FALLACIES. 


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SECTION    XIX. 

PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 

We  have  now  to  consider  what  the  Principles  are 
which  may  be  regarded  as  the  foundations  of  Logic — 
that  is,  the  Principles  which  are  involved,  whether 
exphcitly  or  implicitly,  in  making  assertions,  and  in 
putting  them  together.  Logic,  as  we  have  seen  in 
the  preceding  Sections,  is  concerned  with  statements 
or  propositions— that  is,  assertions  or  judgments 
expressed  in  language — and  with  the  various  relations 
between  such  expressed  judgments.  A  thought  must 
be  formulated  before  it  can  be  entitled  to.be  called 
a  judgment,  and  a  judgment  must  be  expressed 
before  it  can  become  the  subject  of  logical  discussion 
and  investigation. 

The  fundamental  form  of  Proposition  is  the  Cate- 
gorical {cf.  pp.  55,  56);  hence  it  would  appear  that  wc 
need,  in  the  first  place,  a  Principle  of  Categorical 
Assertion.  Now,  we  saw  in  Section  iii.  that  what 
every  Categorical  Proposition  affirms  or  denies  is 
Identity  in  Diversity ;  hence  the  principle  which  we 

202 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC.  203 

are  seeking  must  be  a  Law  of  Identity  in  Diversity. 
This  may  be  expressed  as  follows  :— 

Everything  which  can  be  thought  of  or  named 
is   an  Identity  in  Diversity— (a   Diversity   of 
interdependent  characteristics). 
This    implies   that   every   nameable   thing  has   a 
plurality  of  characteristics,  and  may  be  referred  to  by 
more  than  one  name ;  hence  that  any  name  may  be 
the  Subject  of  a  Categorical  Proposition  of  the  form 
>S'  is  P.     It  impUes  further,  that  in  order  that  any- 
thing should  be  regarded  as  having,  a  character  of 
its  own,  as  being  one  thing  rather  than  a  multiplicity 
of  things,  its  characteristics  must  be  regarded  as  in- 
terdependent—for interdependence  of  characteristics 
seems  inseparable  from  Identity. 

The  Law  of  Identity  in  Diversity  may  be  repre- 
sented by  the  symbolic  statement 

A  is  B. 
It  seems  clear  that  nothing  can  be  thought  of  except 
as  having  (1)  plurality  of  characteristics,  (2)  interde- 
pendence of  characteristics,  (3)  permanence.  Hence 
no  object  can  be  named  which  is  not  regarded  as 
an  Identity  more  or  less  perduring  in  a  Diversity  of 
interdependent  characteristics.  Indeed,  permanence 
itself  involves  Identity  in  Diversity,  for  whatever  is 
permanent,  is  permanent  amid  change ;  and  though 
a  thing  which  has  permanence  is  the  identical  thing 
at  the  end  of  its  duration  that  it  was  at  the  begin- 


204 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


ning,  it  is  also  diverse,  because  at  least  its  ti7)ie- 
characteristics,  and  all  that  they  imply,  have  under- 
gone alteration. 

Further,  anything  that  we  can  think  of  has  to  be 
thought  of  not  only  as  being  itself  a  something,  but 
also  as  connected  with  all  other  somethings,  as  being 
itself  a  part  of  the  universe.  As  every  thing  by  itself 
nuist  be  thought  of  as  an  Identity  in  Diversity,  so 
every  thing  as  a  constituent  of  the  world,  as  a  mem- 
ber of  the  system  of  connected  things  to  which  it 
belongs,  must  be  thought  of  as  related  to  every  other 
member  of  that  system  and  to  the  whole.  Therefore, 
not  only  may  anything  be  called  by  more  names 
than  one,  but  it  may  actually  be  called  by  any  one  of 
the  innumerable  multitude  of  names  which  express 
the  innumerable  multitude  of  relations  (positive  and 
negative)  to  other  things  (Subjects  or  Attributes) 
which  are  among  its  characteristics  (c/.  Law  of  Ex- 
cluded Middle).  Consider,  e.g.,  the  mathematical  rela- 
tions of  a  Conic  Section  to  other  geometrical  figures ; 
or  the  relation  of  any  individual  man  to  his  ancestors 
and  their  descendants ;  or  the  relation  of  any  moment 
to  the  rest  of  time,  or  of  any  position  in  space  to  any 
and  all  other  positions  in  space,  etc. ;  of  one  thought 
of  any  mind  to  the  other  thoughts  of  that  mind  ;  of 
any  quantity  or  colour  to  other  quantities,  colours,  etc. 

Moreover,  the  idea  of  a  world  or  system,  a  whole  of 
connected  parts,  seems  to  involve  uniformity  of  inter- 
dependence between  characteristics.     Not  merely  is 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


205 


this  both  true  of  the  world  as  we  know  it,  and  implied 
in  existing  language  (without  it,  e.g.,  Common  Names 
would  cease  to  be  important  or  even  possible),  but  it 
seems  as  impossible  to  think  of  a  world  without  this 
uniformity,  or  of  an  absence  of  such  uniformity  in 
given  cases,  as  to  think  of  any  single  thing  that  is  not 
an  Identity  in  Diversity.^ 

In  a  whole  that  is  made  up  of  parts,  there  must 
be  Similarity  in  Otherness.     Absolute  Dissimilarity  of 
any  two  things  is  as  completely  unthinkable  as  abso- 
lute Similarity  of  two  things,  and  this  is  a  contradic- 
tion in  terms.     If  absolutely  dissimilar,  things  could 
not  be  compared;   if  absolutely  similar,  they  could 
not  be  distinguishable— would,  in  fact,  be  not  two  but 
one.     And  further.  Similarity  between  any  two  things 
in  one  point  only  is  not  thinkable ;  hence  on  this 
line  of  thought  again  we  are  led  to  the   conclusion 
that   in   any  connected  whole    there   must  be  uni- 
formity of  interdependent  characteristics.    I  hold  that 
the  reason  why  Similarity  between  any  two  things  in 
one  point  only  is  not  thinkable,  is  that  every  charac- 
teristic must  be  thought  of  as  having  (in  Bacon's 
phrase)  its  i^orm— that  is,  an  accompaniment  which 

*  In  the  case  of  organic  things  as  known  to  us,  the  stability  of 
nature  of  an  individual  thing,  and  uniformity  of  co-existent  charac- 
teristics in  distinct  things,  seem  bound  up  together.  For  instance, 
it  is  inconceivable  that  the  seed  of  any  plant  should  develop  into  a 
different  plant— as  an  acorn  into  an  elm,  or  mignonette  seed  into 
candytuft— or  the  egg  of  one  kind  of  bird  hatch  into  another  kind 
of  bird — as  the  egg  of  a  robin  into  a  linnet. 


f"*'''^-'^^''^wiSaftgiaaaBBMi 


206 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


is  inseparable  in  any  given  case,  and  uniform  in  all 
cases. 

The  Law  of  Identity  in  Diversity  appears,  on  reflec- 
tion, to  have  the  characteristic  of  self-evidence.  But 
in  any  case  its  acceptance  is  a  necessary  condition  of 
the  acceptance  of  Propositions  which  are,  at  first 
sight,  self-evident — e.g.  Mathematical  Axioms  and  the 
Law  of  Contradiction.  We  cannot  even  state  any  of 
these  self-evident  propositions,  except  in  dependence 
on  the  Principle  of  Identity  in  Diversity.  For  in- 
stance, the  following  assertions — 

A  whole  is  greater  than  its  parts. 

If  equals  be  added  to  equals,  the  wholes  are  equals. 

If  A  be  B,  A  is  not  not-B — 

would  be  impossible,  unless  each  of  the  Terms  used 
were  the  name  of  an  object  which  is  an  Identity  in 
Diversity.  And  in  as  far  as  the  Principle  of  Interde- 
pendence asserts  merely  that  every  characteristic  is  ac- 
companied by  some  other  characteristic,  it  is  involved 
in  the  Principle  of  Identity  in  Diversity  (and,  therefore, 
in  the  Law  of  Contradiction).  And,  as  a  Principle  of 
UnifoTTnity,  it  is  also  involved  in  the  Law  of  Contra- 
diction, as  far  as  interdependence  of  the  presence  of 
B  and  the  absence  of  not-B  is  concerned,  and  up  to 
this  point  appears  to  be  immediately  self-evident. 
Further,  Uniformity  of  Interdependence  is,  at  first 
sight,  self-evident  in  the  case  of  Mathematical  In- 
ductions. 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


207 


The  Law  of  Identity  in  Diversity,  and  the  axioms 
referred  to  on  p.  147,  may  be  formulated  as  follows : — 

(1)  Every   thing    has    a    plurality   of    interde- 

pendent characteristics. 

(2)  No  two  things  have  only  one  characteristic 

similar.^ 
(8)  No  two  things  have  only  one  characteristic 
different. 

(4)  No  two  things  have  all  characteristics  similar. 

(5)  No     two     things    have    all    characteristics 

different.*' 

The  last  four,  as  well  as  the  first,  appear  to  me  to 
be,  on  reflection,  self-evident — to  carry  their  own 
evidence  with  them,  and  not  to  need  the  support  of 
other  propositions.  The  Principle  of  Interdependence 
is  substantially  a  formulation  of  (2)  and  (3) ;  and  (2), 
(8),  (4),  (5),  taken  together  atnount  to  this :  that  any 
two  things  are  alike  in  a  plurality  of  points,  and  that 
any  two  things  are  also  unlike  in  a  plurality  of  points. 

It  is  such  relations  of  likeness  and  unlikeness  that 
make  it  possible  to  group  things  together  in  classes. 

1  Among  the  characteristics  of  any  thing  may  be  a  capacity  of 
development;  or  of  variableness  in  certain  respects.  Ej/.  many 
flowers  and  animals  are  variable  in  colour  and  size.  But  every 
variation  of  colour  or  size  must  be  regarded  as  inseparable  from 
other  characteristics.  For  instance,  with  difference  of  colour  go 
differences  of  molecular  structure,  differences  in  light-waves  as 
regards  heat,  rapidity  of  vibration,  and  chemical  action,  difference 
of  complementary  colours,  etc. ,  etc. 

'^  Of.  Index,  under  Identity  of  Indiscernihles,  Laiv  of  Heterogeneity , 
Law  of  1 1  omogtneity . 


■mfiiiiiiMm 


mttim 


208 


PRIN'CIPLES  AND  CATEGORIES  OF  LOGIC. 


The  Law  of  Contradiction — 

A  Proposition  and  its  Negative  (whether  Con- 
trary or  Contradictory)  cannot  both  be 
affirmed;  or, 

If  A  is  B,  A  is  not  not-B — 
is  by  some  logicians  regarded  as  the  most  fundamental 
of  all  logical  principles.    This,  as  we  have  seen,  it  is  not, 
and  cannot  be ;  but  it  may  perhaps  be  admitted  to  be 
that  which  is  most  directly  serviceable  in  dealing  with 
the  connectkms  of  propositions.     A  recent  writer  (Mr. 
Richard  F.  Clarke,  S.J.,  Logic,  pp.  34,  35)  says  that 
"  on  this  Principle  of  Contradiction  all  proof  is  based, 
direct  and  indirect.    ...    It  is  a  necessity  of  our 
reason.     He  who  refuses  to  acknowledge  its  univer- 
sal supremacy  commits  thereby  intellectual  suicide. 
He  puts  himself  outside  the  class  of  rational  beings. 
His  statements  have  no  meaning.     For  him,  truth 
and  falsity  are  mere  words.     According  to  him,  the 
very  opposite  of  what  he  says  may  be  equally  true. 
If  a  thing  can  be  true  and  false  at  the  same  time,  to 
what  purpose  is  it  to  make  any  assertion  respecting 
any  single  object  in  the  universe  ?     Fact  ceases  to  be 
fact,  truth  ceases  to  be  truth,  error  ceases  to  be  error. 
We  are  all  right  and  all  wrong.    What  is  true  is  false, 
what  is  false  is  true.     Statement  and  counterstate- 
ment  do  not  in  the  least  exclude  one  another.     What 
one  man  denies,  another  man  may  assert  with  equal 
truth ;  or  rather,  there  is  no  such  thing  as  Truth  at  all. 
Logic  is  a  Science,  yet  not  a  Science.     The  Laws  of 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


209 


Thoudit  are  universal,  yet  not  universal.  Virtue  is 
to  be  followed,  yet  not  to  be  followed.  I  exist,  yet  I 
do  not  exist.  There  is  a  God,  yet  there  is  no  God^ 
Every  statement  is  false  and  not  false,  a  lie  yet  not  a 
lie.  It  is  evident  that  the  outcome  of  all  this  can  be 
nothing  else  than  the  chaos  of  scepticism  pure  and 
simple— a  scepticism,  too,  which  destroys  itself  by  its 
own  act.  If  the  Law  of  Contradiction  can  be  set 
aside  in  a  single  case,  all  religion,  all  philosophy,  all 
truth,  all  possibility  of  consequent  thinking  disappear 

for  ever." 

The  Law  of  Excluded  Middle  may  be  expressed  as 

follows : — 

A    Proposition    and    its    formal    Alternative 
(whether    Contradictory    or    Sub-contrary) 
cannot  both  be  denied ;  or, 
A  is  B,  or  A  is  not  B. 
The  Law  of  Identity  in  Diversity  may  be  regarded 
as    the    Principle   of    the   possibiHty   of    Significant 
Assertion,  the  Law  of  Contradiction  as  the  Principle 
of  Consistency,  and  the  Law  of  Excluded  Middle  as  a 
Principle  of  Alternation  or  Completion. 

To  the  above  Principles  must  be  added  as  a  Prin- 
ciple of  Induction  the  Law  of  Interdependence,  with 
its  two  branches,  the  Law  of  Concomitance  of  Char- 
acteristics, and  the  Law  of  Causation  of  Events.  (Tlie 
close  connection  of  these  latter  with  the  axioms  of 
Similarity  and  Dissimilarity  has  been  spoken  of  above.) 
We  ought,  also,  to  include  here  a  statement  which 

o 


|l 


ie^mski^MMii^iM 


210 


PRINCIPLES  AND  CATEGORIES  OF  LOGIC. 


sums  up  roughly  the  assumptions  on  which  the 
Inductive  Methods  are  based — the  rule,  namely,  that 
Phenomena  which  are  never  found  separate  from 
each  other  (being  either  Co-existent,  Successive,  or 
Co-variant)  are  Interdependent.  It  is  by  the  help  of 
these  Methods  that  we  determine  the  all-important 
question.  What  are  the  characteristics  which  in  any 
given  case  are  inseparable  ? 

All  Absolute  (or  Non-Relative)  Inference,  is  based 
entirely  on  the  Principle  of  Identity  in  Diversity — it 
is  because  Names  have  Identity  of  Application  in 
Diversity  of  Signification,  that  one  name  may  not  only 
be  asserted  of  another  in  a  Proposition,  but  also  sub- 
stituted for  another  in  Inference.  For  instance,  it  is 
because  M  and  P  have  Identical  Application  that  I 

can  assert 

M  is  P ; 

and  it  is  because  M,  P,  and  S  have  Identity  of 
Application  (in  Diversity  of  Signification),  that  I  am 
able  from  the  Premisses 

MisP 

SisM 

to  conclude 

Sis  P. 

For  Relative  Inference,  however,  we  require  also 
Principles  of  Interrelation — the  Principles,  namely, 
that  (1)  All  Interrelation  is  reciprocal,  (2)  Any  objects 
that  are  related  indirectly  or  mediately,  are  also 
related  directly.  (I)  enables  me  to  infer  that  if  A  is 
related  to  B,  then  B  is  related  to  A ;  (2)  justifies  me 


CATEGORIES  OF  LOGIC. 


211 


in   concluding  that   if  A  is  related   to  B,  and  B  is 
related  to  C,  then  A  is  related  to  C. 

Finally,  the  Principle  of  Self-Evidence — What  is 
self-evident  ought  to  be  believed — appears  to  be  the 
most  absolute  and  ultimate  of  all  logical  principles. 


CATEGORIES  OF  LOGIC. 

The  fundamental  Category  of  Logic  is  Unity  in 
Difterence  (taking  Unity  to  include  both  Identity  and 
Similarity,  Difference  to  include  both  Dissimilarity 
and  Numerical  Distinctness).  Most  of  the  wide 
notions  chiefly  used  in  Logic  come  under  this  head. 
Every  thing  spoken  of  is  an  Identity  in  Diversity; 
every  Categorical  Proposition  is  an  affirmation  or 
denial  of  Identity  in  Diversity.  In  Substance  and 
Attribute,  Existence  and  Character,  in  Interdependence 
(Concomitance — Causation),  in  Alternation,  in  all 
Inference,  we  have  Identity  in  Diversity.  Quantity 
is  an  Attribute  of  Substances,  a  mere  Quality  among 
other  Qualities,  and  the  action  and  passion  and  change 
of  any  Substance  is  among  its  Attributes ;  all  Relation 
is  Unity  in  Difference ;  the  Category  of  Classing,  and 
of  Inductive  (in  as  far  as  distinguished  from  Deductive) 
Inference  is  Similarity  in  Otherness ;  Classification  and 
Systematisation  involve  the  three  kinds  of  Unity  in 
Difference,  namely,  Identity  in  Diversity,  Similarity 
in  Otherness,  the  Unity  of  Whole  and  Parts;  all 
Fallacy  is  reducible  to  mistaken  assertion  of  Identity 
or  Distinctness. 


NOTES. 


L 


'opposition'  of  propositions. 

Categorical  Propositions  which  have  the  same  Subject- 
name  and  the  same  Predicate-name,  but  differ  in  Quantity  or 
Quality,  or  in  both  Quantity  and  Quality,  are  technically 
said  to  be  opposed  to  each  other.  This  Opposition  of  pro- 
positions is  illustrated  by  the  ancient  diagrammatic  device 
called  the  Square  of  Opposition,  which  is  represented  below. 


(All  R  is  Q)  A 


Contraries 


E  (No  R  is  Q) 


(Some  R  is  Q)  I  «ub-contra,ries  0  (Some  R  is  not  Q) 


A  and  E  are  called  Contraries 


I 


?) 


0 


>5 


Sub-contraries 


213 


Nl 


laiiitiirffiMir"'^'-"-*---^ 


■^^^bfa^feiiia. 


ggl^ij^lgj 


214 


A  and  I 
E     „    O 


A 

E 


} 

„    01 


NOTES. 


are  called  Subalterns 


?5 


Contradictories. 


Contraries  cannot  both  be  true,  but  may  both  be  false. 

Sub-contraries  cannot  both  be  false,  but  may  both  be  true. 

Contradictories  cannot  both  be  true,  and  cannot  both  be 
false. 

Of  Subalterns,  if  the  Universal  is  true.,  the  Particular  is 
true  ;  if  the  Particular  is  false,  the  Universal  is  false. 

Contraries  differ  in  Quality  but  not  in  Quantity. 

Sub-contraries  differ  in  Quantity  but  not  in  Quality. 

Contradictories  differ  in  both  Quantity  and  Quality. 

It  is  only  Categoricals,  and  of  them  only  Class  Cate- 
goricals,  that  are  contemplated  in  the  traditional  doctrine  of 
Opposition,  and  the  illustrative  Square. 


II. 


THE    PREDICABLES. 


The  Predicables  are  a  classification  of  Predicates  considered 
in  relation  to  their  subject-names.  The  ancient  doctrines  of 
Predicables  were  connected  with  what  is  called  the  Realist 
hypothesis — the  view,  that  is,  that  there  is  in  nature  a  system 
of  Universals  corresponding  to  every  general  (or  class)  notion, 
and  entering  into  the  composition  of  each  member  of  a  class 
— membership  of  the  class  depending  upon  participation  in 
the  corresponding  Universal.  On  this  view,  classes  are  dis- 
covered by  man,  not  made  by  him,  and  an  Infima  Species  (or 
Lowest  Class),  and  a  Summum  Genus  (or  Highest  Class)  are 
possible. 


NOTES. 


215 


Aristotle    adopted    a   four-fold    division   of    Predicables, 
namely — 

1.  Definition. 

2.  Proprium. 

3.  Genus. 

4.  Accidens. 

In  any  propositions  predicating  Definition  or  Proprium, 
Subject-name  and  Predicate-name  are  convertible,  because 
they  have  the  same  application  ;  in  any  Proposition  predicat- 
ing Genus  or  Accidens,  Subject-name  and  Predicate-nanje  are 
not  convertible,  because  the  application  is  not  coincident. 
In  (1)  signification  (or  connotation)  of  Subject-name  and 
Predicate-name  are  substantially  similar;  in  (3)  they  are 
partly  similar ;  in  (2)  and  (4)  entirely  diverse. 

The  following  propositions  may  be  given  as  examples — 

(1.)  Man  is  a  rational  animal. 

(2.)  Man  is  capable  of  laughter, 

(3.)  Man  is  an  animal. 

(4.)  Man  is  two-handed. 

Gemts  means  a  class  in  which  narrower  classes  are  con- 
tained;  e.g.  the  class  Animal,  which  contains  Man  and 
Brute  is  a  Genus. 

Proprium  means  some  quality  that  results  from  the 
Definition  (e.g.  capacity  for  laughter  results  from  the  attri- 
bute of  rationality). 

Accidens  means  some  Attribute  which  belongs  to  the 
members  of  the  class,  but  neither  is  connoted  by,  nor  follows 
from,  Genus  or  Definition.  Definition  expresses  the  con- 
notation of  the  Genus  of  the  class  defined  -f  connotation  ivhich 
distinguishes  that  class  from  the  other  classes  contained  in  the 

Genus. 

But  this  four-fold  scheme  of  Aristotle's  was  replaced  by  a 


210 


NOTES 


later  tive-fold  classification  introduced  by  the  Neo-platonist 
Porphyry  in  the  third  century.  According  to  this  account 
the  Predicables  are  as  follows  : — 

(1.)  Genus. 

(2.)  Species. 

(3.)  Differentia  (Difference). 

(4.)  Proprium  (Property). 

(5.)  Accidens  (Accident). 

For  of  any  Subject  we  can  predicate  (1)  a  wider  containing 
class ;  (3)  the  differentiating  attribute  by  which  the  Subject 
is  marked  off  from  the  rest  of  the  Genus;  (2)  Genus  (1)  + 
Differentia  (3) ;  (4)  some  characteristic  which  follows  from  the 
signification  of  (1)  or  (3);  (5)  some  characteristic  which  belongs 
to  the  Subject,  but  neither  follows  from,  nor  is  included  in, 
the  connotation  of  Genus  or  Differentia. 

If  we  take  the  species  Man,  its  Genus  (as  before)  is 
Animal;  its  Differentia  is  Rational  (and  Genus  -j-  Differ- 
entia =  Species) ;  a  Proprium  is  cooking  his  food ;  an 
Accident  is,  smooth-skinned.  This  Accident  is  Inseparable, 
because  common  to  all  men.  Having  woolly  hair  would  be  a 
Separable  Accident  of  the  class  Man,  because  it  is  an  Attri- 
bute of  some  men  only.  Separable  and  Inseparable  Acci- 
dents of  Individuals  are  also  spoken  of.  E.g.  it  would  be 
an  Inseparable  Accident  of  Virgil  that  he  was  born  at 
Mantua,  a  Separable  Accident  that  he  is  hungry  or  awake. 

In  Plato  is  a  man  we  predicate  Species  Praedicahilis. 

In  Man  is  an  animal,  Man  is  Species  Suhjicihilis. 

The  whole  scheme  is  somewhat  remote  from  our  present 
needs  and  modes  of  thought. 

Tree  of  Porphyry. 

This  is  the  name  usually  given  to  a  diagrammatic  device 
attributed  to  Porphyry,  and  illustrative  of  the  Predicables 
and  their  relation  to  Division  and  Definition.     It  is  called 


NOTES. 


217 


also  the  Ramean  Tree,  after  the  reforming  sixteenth-century 
logician  Ramus. 


-'  ^- 


v^<-' 


of- 


*^ 


V 


^x-^"'..C^^" 


^-<o.^^ 


^^^''  ^0^-^ 


SUBSTANCE 


In  this  diagram  we  start  from  Substance,  which  is  the 
Summum  Genus,  the  highest  (or  widest)  class,  and  finish  with 
individual  members  of  the  class  Man,  which  is  an  Infima 
Species,  the  lowest  (or  narrowest)  class  that  we  reach  in  the 
process  of  subdivision.  The  line  of  ascent  through  the 
positive  members  of  the  division — Corporeal,  Body,  Organic, 
Living  thing.  Sensitive,  Animal,  Rational,  to  Man — is 
called  the  Predicamental  Line.  At  each  step  the  division  is 
by  Dichotomy  (twofold  division)  into  a  class  and  its  negative 
(Corporeal,  Incorporeal,  etc.).  A  division  by  Dichotomy  is 
necessarily  exhaustive,  as  (by  the  Principle  of  Excluded 
Middle)  whatever  does  not  belong  to  the  positive  branch 
must  belong  to  the  negative  one.     The  addition  to  the  Genus 


,sf| 


218 


NOTES. 


Substance  of  the  Dift'erentia  Corpoi-eal,  gives  the  Species 
Body.  When  Body  is,  in  its  turn,  divided  into  Organic  and 
Inorganic,  it  becomes  Genus  to  those  two  Species ;  and  so 
on  throughout,  until  we  reach  the  Infima  Species  Man, 
which  can  only  be  divided  into  individuals.  Body,  Living 
thing,  and  Animal  (which  are  alternately  Species  and  Genera), 
are  called  Subaltern  Genera  and  Species.  Every  class  is  a 
Genus  to  all  the  classes  narrower  than  itself ;  and  to  every 
class  the  next  wider  one  is  a  Proxiraum  Genus,  e.g.  Animal 
is  the  Proximum  Genus  to  Man. 

in. 

'  PERFECT    INDUCTION. ' 

This  name  has  been  given  to  an  argument  in  which  a 
number  of  things  are  enumerated  one  by  one  in  the  Pre- 
misses, and  summed  up  under  a  general  expression  in  the 
Conclusion.  The  following  argument  is  one  of  the  examples 
given  by  Jevons  of  a  '  Perfect  Induction ' : — 

Mercury,  Venus,   the  Earth,  etc.,  all  move  round  the 

Sun  from  West  to  East ; 
Mercury,  Venus,  the  Earth,  etc.,  are  all  (  =  the  whole  of) 

the  known  Planets ; 
Therefore   all    (  =  each    of)   the    known    Planets   move 
round  the  Sun  from  West  to  East. 

— (Jevons,  Elementary  Lessons  in  Logic,  pp. 
214,  215.) 
The  syllogistic  expression  of  the  argument,  as  above,  has 
been  called  an  '  Inductive  Syllogism ' ;  but  its  scope  is  en- 
tirely different  from  that  of  the  reasoning  by  which  we  arrive 
at  a  fresh  generalisation  or  law. — Cf.  ante,  pp.  81,  84-85, 
87,  136,  etc. 

As  far  as  I  have  observed,  in  all  the  examples  of  '  Perfect 
Induction '  which  are  given  by  different  logicians,  there  is  the 
curious  flaw  that  the  Minor  Term  is  taken  collectively  in  the 
Minor  Premiss  and  distributively  in  the  Conclusion. — *  Perfect 


NOTES. 


219 


Induction '  is  also  known  as  Aristotelian  Induction,  Formal 
Induction,  Complete  Induction. 

IV. 

ELLIPTICAL    AND    COMPOUND    ARGUMENTS. 

In  ordinary  speech  and  writing  arguments  are  frequently 
not  expressed  at  full ;  for  instance,  we  constantly  hear  such 
abbreviated  Syllogisms  as — 

(1)  This  fungus  is  a  true  mushroom,  therefore  it  is  good 
to  eat. 

(2)  All  cows  are  ruminants,  therefore  this  animal  is  a 
ruminant. 

(3)  All  bullies  are  hateful,  and  this  boy  is  a  bully. 

In  (1)  the  suppressed  proposition  is  the  Major  Premiss, 
All  true  mushrooms  are  good  to  eat ;  in  (2)  it  is  the  Minor 
Premiss,  This  animal  is  a  cow ;  in  (3)  it  is  the  conclusion, 
This  boy  is  hateful.  Elliptical  arguments  of  this  sort  are 
frequently  called  Enthymemes  (e.g.  by  Jevons  and  Whately). 
Where  the  Major  is  suppressed,  the  Enthymeme  is  said  to  be 
of  the  First  Order ;  where  the  Minor  is  suppressed,  it  is  of 
the  Second  Order ;  where  the  Conclusion  is  suppressed,  it  is 
of  the  Third  Order. 

There  is  an  interesting  correspondence  between  these  in- 
complete arguments  and  Inferential  Syllogisms  of  the  forms — 

If  Mis  P,  SisP(-.-SisM). 

If  SisM,  SisP(-.-MisP). 

(Cf.  ante,  pp.  45,  46.) 

The  argument  which  is  called  Sorites  or  Chain-argument 

is  also  enthymematic. 

It  is  of  two  forms,  e.g. — 

(1)  All  As  are  B's. 

All  B's  are  C's. 

All  C's  are  D's. 

All  D's  are  E's. 

.  •.  All  A's  are  E's. 


MUinjutti&njlBh^^M 


iMaaMiaaniaaBi 


aWBariilBaiSBMffiilllWMl^ 


220 


NOTES. 


(2)  All  D  is  E. 
All  C  is  D. 
All  B  is  C. 
All  A  is  B. 


.  •.  All  A  is  E. 

(1)  is  called  a  Progressive  Sorites, 

(2)  a  Regressive  or  Goclenian  Sorites. 

In  (1)  there  may  be  one  Particular  Premiss,  provided  it 
be  the  first,  and  one  Negative  Premiss,  provided  it  be  the 
last.  In  (2)  there  may  also  be  one  Negative  Premiss  (the 
first),  and  one  Particular  Premiss  (the  last).  Thus,  in  the 
examples  given,  A-B  may  be  Particular,  D-E  may  be 
Negative. 

The  relations  of  Terms  may  be  represented  by  e.g.  the 
following  circles,  thus 


NOTES. 


221 


In  (a)  all  the  Propositions  are  Affirmative  and  Universal ; 
in  (6)  one  is  Particular,  and  one  is  Negative. 

(a)  and  (6)  can  each  be  resolved  into  a  series  of  dependent 
Syllogisms,  as  follows  : — 

(a)      (i.)  All  B  is  C. 
All  A  is  B. 

All  A  is  C. 

(ii.)  All  C  is  D. 

All  A  is  C. 


All  A  is  I). 

(iii.)  All  D  is  E. 

All  A  is  D. 


All  A  is  E. 
This  is  a  Progressive  Sorites. 

{h)      (i.)  No  D  is  E. 
All  C  is  D. 

NoCisE. 

(ii.)  No  C  is  E. 

All  B^is  C. 

~No  B^is  E. 

(iii.)  No  B  is  E. 

Some  A  is  B. 

Some  A  is  not  E. 
This  is  a  Regressive  Sorites. 

It  will  be  seen  that  in  («)  the  conclusion  of  each  Syllogism 
of  the  chain  furnishes  the  Minor  Premiss  of  the  next  Syllo- 
gism; (i.)  is  therefore  a  Pro-syllogism  to  (ii.),  and  (ii.)  is  a 
Pro-syllogism  to  (iii.);  while  reciprocally  (iii.)  is  Episyllo- 
gism  to  (ii.),  and  (ii.)  is  Episyllogism  to  (i.). 

Correspondingly  in  (6),  every  conclusion  furnishes  the 
Major  Premiss  to  the  next  Syllogism  in  the  series,  and  the 
relations  of  Pro-syllogism  and  Episyllogism  hold  between 
(i.),  (ii.),  and  (iii.). 


riii^iMiiiiitaiiiilffiHii^ 


at-  '^-■^--'•-■'iiiiiiiiii 


222 


NOTES. 


A  Sorites  may  equally  well  be  Inferential  or  Alternative. 
An  Epicheirema  is  a  compound  and  elliptical  syllogism,  in 
which  to  one  or  both  Premisses  there  is  attached  a  reason 
implying  the  existence  of  a  Pro-syllogism  which  is  not  fully 
expressed.     E.g. — 

M  is  P  (for  it  is  Q) ; 
S  is  M  (for  it  is  R) ; 
.-.Sis  P. 


V. 


THE    '  DEDUCTIVE   METHOD '    OF    INDUCTION. 

Besides  the  Methods  of  Induction  described  in  Section  xiii. 
{rf.  also  post,  Note  vi.),  there  is  a  Method  of  establishing 
Inductive  generalisations  which  is  described  by  Mill  under 
the  name  of  '  The  Deductive  Method.'  Jevons  considers  that 
this  might  be  more  appropriately  called  the  '  Combined '  or 
*  Complete '  method  ;  and  it  corresponds  very  closely  to  what 
he  regards  as  the  true  Method  of  Inductive  Reasoning. 

The  *  Deductive  Method '  deals  not  with  Simple  but  with 
Complex  Effects,  and  '  its  problem  is  to  find  the  law  of  a 
complex  effect  from  the  laws  of  the  different  causes,  of  which 
this  effect  is  the  joint  result.'  The  first  step  is  to  ascertain, 
by  separate  applications  of  Induction,  the  effect  of  each  of 
the  causes  concerned  in  the  joint  result.  (We  might  resolve 
this  step  into  Observation,  Hypothesis,  and  the  application  of 
the  '  Methods  of  Experimental  Inquiry  ' — Method  of  Agree- 
ment, etc.)  The  second  step  is  Ratiocination  (or  Calculation, 
or  Deduction),  from  the  several  simple  laws  to  the  complex 
case.  The  third  step  consists  in  the  Verification  of  the 
results  arrived  at  by  the  second  step. 

A  stock  illustration  of  the  '  Deductive  Method '  is  furnished 
by  the  *  Parallelogram  of  Forces.'     We  suppose  a  particle  Q 


NOTES. 


228 


at   A  to  be  acted   upon  by   two  forces  R  and  C,  and  the 
problem  is,  to  find  the  joint  effect  of  B  and  C  from  a  know- 


ledge of  the  effect  of  B  separately  and  C  separately.  We 
find  that  B  would  carry  Q  from  A  to  D  in  time  T ;  and  that 
C  would  carry  Q  from  A  to  F  in  time  T.  (This  is  the  first 
step.) 

We  argue  that,  therefore,  if  B  and  C  acted  together,  they 
would  in  time  T  carry  Q  as  far  as  D  in  the  one  direction, 
and  as  far  as  F  in  the  other.  The  point  E  is  as  far  from  A 
as  D  on  the  one  hand,  and  as  F  on  the  other. 

.*.  B  and  C  will  carry  Q  from  A  to  E  in  time  T.  This  is 
the  second  step. 

The  Verification  might  consist  in  taking  a  particle  Q  at  A, 
and  causing  B  and  C  to  act  upon  it  simultaneously.  If  at 
the  end  of  T,  Q  is  at  E,  the  third  step  (and  with  it  the 
Verification)  has  been  accomplished. 

There  are  several  variations  of  the  '  Deductive  Method ' ; 
for  instance,  the  Verification  may  be  by  direct  appeal  to  fresh 
experience  (as  above) ;  or  by  appeal  to  the  recorded  results  of 
previous  experience  (as  Newton's  theory  of  gravitation  was  to 
some  extent  verified  by  its  agreement  with  Kepler's  Laws). 


224 


NOTES 


VI. 


mill's    canons    of     his     '  FOUR    METHODS    OF    EXPERIMENTAL 

[  =  experiential]    INQUIRY.' 

First  Canon — I.  Method  of  Agreement  : 

If  two  or  more  instances  of  the  phenomenon  under  in- 
vestigation have  only  one  circumstance  in  common,  the 
circumstance  in  which  alone  all  the  instances  agree,  is  the 
cause  (or  effect)  of  the  given  phenomenon. 

Second  Canon — II.  Method  of  Difference  : 

If  an  instance  in  which  the  phenomenon  under  investiga- 
tion occurs,  and  an  instance  in  which  it  does  not  occur,  have 
every  circumstance  in  common  save  one,  that  one  occurring 
only  in  the  former;  the  circumstance  in  which  alone  the 
two  instances  differ  is  the  effect  or  the  cause,  or  an  indis- 
pensable part  of  the  cause,  of  the  phenomenon. 

Third  Canon — Joint  Method  of  Agreement  and  Difference: 

If  two  or  more  instances  in  which  the  phenomenon 
occurs  have  only  one  circumstance  in  common,  while 
two  or  more  instances  in  which  it  does  not  occur  have 
nothing  in  common  save  the  absence  of  that  circumstance ; 
the  circumstance  in  which  alone  the  two  sets  of  instances 
differ  is  the  effect,  or  the  cause,  or  an  indispensable  part  of 
the  cause,  of  the  phenomenon. 

(This  method  is  also  called  briefly  the  Joint  Method,  or  the 
Method  of  Agreement  in  Presence  and  Absence,  or  the  Indirect 
Method  of  Difference.  It  is  not  reckoned  by  Mill  as  a  separate 
Method.) 


NOTES. 


225 


Fourth  Canon — III.  Method  of  Residues  : 


Subduct  from  any  phenomenon  such  part  as  is  known  by 
previous  inductions  to  be  the  effect  of  certain  antecedents, 
and  the  residue  of  the  phenomenon  is  the  effect  of  the  remain- 
ing antecedents. 

Fifth  Canon — IV.  Method  of  Concomitant  Variations  : 

Whatever  phenomenon  varies  in  any  manner  whenever 
another  phenomenon  varies  in  some  particular  manner,  is 
either  a  cause  or  an  effect  of  that  phenomenon,  or  is  con- 
nected with  it  through  some  fact  of  causation. 


•  I 

i 


QUESTIONS    AND    EXERCISES 


SECTION    I. 


1.  Discuss  the  scope  and  definition  of  Logic  ;  and  show  how  the 
definition  which  you  accept  can  be  applied  in  the  various  depart- 
ments of  Logic. 

2.  What  (if  any)  are  the  assumptions  of  ordinary  Logic  ? 

3.  What  do  you  understand  by  Science  ? 

In  what  sense  is  Logic  a  Science,  and  what  is  its  relation  to  other 
Sciences  ? 

4.  In  what  sense  may  Logic  be  called  the  Science  of  Sciences  ? 

(J.) 

SECTION    IL 

5.  Define  Fwposition^  and  enumerate  the  different  kinds  of 
Propositions,  with  examples. 

6.  How  is  it  that  an  examination  of  Names  and  Terms  comes 
under  the  head  of  *  Import  of  Propositions '  ? 

What  do  you  understand  by  hnport  of  Propositions  ? 

7.  Define  Name ;  and  describe  the  diff'erent  kinds  of  Names, 
with  examples. 

8.  Can  you  suggest 

(a)  Any  explanation 

(6)  Any  justification 
for  the  fact  that  (in  English  and  other  languages)  we  find  three 
distinct  classes  of  Names,  viz.  : — 

(1)  Substantival  Names  (e.g.  man) 

(2)  Attribute  Names  (e.g.  humanity) 

(3)  Adjectival  Names  {e.g.  human)  ? 

226 


^ 


QUESTIONS  AND  EXERCISES. 

9,  What  is  meant  by 

(a)  Application 

(b)  Signification 

of  Names  and  Terms  ?    Illustrate  your  answer  by  examples. 

10.  Give  a  logical  description  of  the  following  names  : — 


227 


Fog — Whiteness. 

Violet — Fragrant. 

King  of  Spain. 

January. 

The  four  elements. 

Strong — Splendour. 

Equal  to  B. 


William  Shakspeare. 

The  Thames. 

The  highest    mountain    in    the 

The  sun.  [world. 

Wordsworth. 

Lion. 


Fairy. 

11.  What  is  meant  by  saying  that  the  application  and  force  of 
words  depends  upon  context  ?  Is  this  an  absolute  and  unvarying 
rule  ?    Illustrate  by  reference  to  the  Dictionary. 

12.  Define  Term,  and  give  a  tabulated  list  of  the  principal 
kinds  of  terms. 

13.  Discuss  the  importance  of  the  distinction  between  Absolute 
and  Relative  Terms. 

14.  Distinguish  between 

(a)  Collective  and  Non-collective  Names 
(6)  Collective  and  Distributive  use  of  Names. 

Point  out  the  Collective  and  Distributive  use  of  the  word  All  in 

the  following : — 

(1)  All  the  angles  of  a  triangle  are  equal  to  two  right  angles. 

(2)  All  the  angles  of  a  triangle  are  less  than  two  right  angles. 

(3)  All  men  find  their  own  in  all  men's  good, 
And  all  men  join  in  noble  brotherhood. 

SECTION   in. 

15.  Give  an  Analysis  and  a  Definition  of  Categorical  Proposi- 
tions, with  examples. 

16.  Draw  up  a  Table  of  the  principal  kinds  of  Categorical  Pro- 
position. 

17.  Distinguish  between  the  relations 

(a)  Of  Terms 

(b)  Of  Classes. 


228 


QUESTIONS  AND  EXERCISES. 


18.  What  do  you  consider  to  be  the  essential  distinctions  be- 
tween the  Subject  and  Predicate  of  a  Proposition  ?  Apply  your 
answer  to  the  following  : — 

The  lake  of  Geneva  is  blue. 
That  is  exactly  what  I  wanted. 
Great  is  Diana  of  the  Ephesians. 
Twenty-four  prisoners  were  released. 
All  pedants  are  absurd. 

(C.  somewhat  altered.) 

19.  Determine  the  Subject  of  the  Proposition,  'Cambridge  is 
the  winner.'  Is  it  true  to  say  that  'an  Adverb  cannot  form  the 
Subject  of  a  Proposition'  ?  If  so,  what  is  the  subject  of  the  Pro- 
position you  have  declared  to  be  true  ? 

(C.  shortened.) 

20.  Examine  the  following  statements  : — 

(1)  When  we  refer  vaguely  to  X  we  always  mean  All  X  or 
Some  X. 

(2)  Even  '  Some  X  '  means  All  of  that  Some. 

(C.  modified.) 

21.  Distinguish  Universal  and  Particular  Categorical  Proposi- 
tions.    Determine  the  Quantity  of  each  of  the  following  : — 

(1)  The  king  is  dead. 

(2)  None  need  despair. 

(3)  All  that  glitters  is  not  gold. 

(4)  One  Trinity  man  was  in  the  first  class. 

(C.) 

22.  Take  the  following  Propositions,  and  put  them  into  proper 
logical  form,  pointing  out  the  Subject  and  Predicate  in  each 
case  : — 

(1)  All  day  long  the  noise  of  battle  rolled 
Among  the  mountains. 

(2)  In  truth  we  have  lived  carelessly  and  well. 

(3)  Into  the  street  the  piper  stepped, 
Smiling  first  a  little  smile. 

(4)  With  Time  I  have  no  quarrel. 

(5)  Every  why  hath  a  wherefore. 

(6)  Only  the  brave  deserve  the  fair. 

(7)  A  stitch  in  time  saves  nine. 

(8)  All  men  find  their  own  in  all  men's  good. 


QUESTIONS  AND  EXERCISES. 


229 


(9)  He  jests  at  scars  who  never  felt  a  wound. 

(10)  Every  mistake  is  not  culpable. 

(11)  Few  men  attain  celebrity. 

(12)  He  can't  be  wrong  whose  life  is  in  the  right. 

(13)  No  news  is  good  news. 

(14)  All  is  fine  that  is  fit. 

(15)  All  is  not  gold  that  glitters. 

(16)  There  are  three  things  to  be  considered. 

(17)  James  misunderstood  Thomas. 

(18)  A  few  of  the  apples  are  ripe. 

23.  Give  a  logical  description 

'{a)  Of  the  following  Propositions 
(6)  Of  their  Terms  :— 

(1)  Every  mistake  is  not  a  proof  of  ignorance. 

(2)  Any  schoolboy  could  tell  you  that. 

(3)  Life  every  man  holds  dear. 

(4)  Spring,  Summer,  Autumn,  and  Winter  are  the  four  seasons. 

(5)  Nothing  in  his  life 

Became  him  like  the  leaving  it. 

(6)  He  who  fights  and  runs  away 
Will  live  to  fight  another  day. 

(7)  No  one  is  a  hero  to  his  valet. 

(8)  None  think  the  great  unhappy  but  the  great. 

(9)  Honesty  is  the  best  policy. 

(10)  Aglaia,  Thalia,  and  Euphrosyne  were  the  three  Graces. 

(11)  Snowdon  is  the  highest  mountain  in  Wales. 

(12)  Those  trees  are  oaks. 

(13)  2  +  2  =  4. 

(14)  A  is  equal  to  B. 

(15)  C  is  larger  than  D. 

(16)  Philip  was  the  father  of  Alexander. 

(17)  Some  mistakes  are  a  proof  of  genius. 

(18)  A  bargain 's  a  bargain. 

(19)  Some  kindness  is  cruel. 

(20)  Some  wisdom  is  folly. 

(21)  To  err  is  human. 

(22)  To  him  that  will,  ways  are  not  wanting. 

(23)  All 's  well  that  ends  well. 

(24)  Some  death  is  better  than  some  life. 

(25)  2  +  5-1=2x3. 


ItlfiiiiliMl^liiiMiiilBiairiira 


230 


QUESTIONS  AND  EXERCISES. 


SECTION    IV. 


24.  Discuss  the  nature  of  the  difference  between  Relative  and 
Absolute  Propositions,  and  consider  the  logical  importance  of  this 
distinction. 

25.  How  would  you 

(1)  class 

(2)  interpret 
Mathematical  Propositions  ? 

t 

SECTION   V. 

26.  Define  Inferential  Pmposition. 

27.  Exhibit  the  elliptical  character  of  Hypothetical  Propositions 
which  are  not  Self-contained. 

28.  Explain  fully  the  distinction  between  Hypothetical  and 
Conditional  Propositions  ;  and  determine  which  of  the  followino- 
propositions  are  Hypothetical  and  which  Conditional :"—  ° 

(1)  If  all  men  were  capable  of  perfection,  some  would  have 
attained  it. 

(2)  If  this  is  admitted,  the  logical  question  is  disposed  of. 

(3)  If  any  beggar  comes  to  the  door,  he  is  to  have  a  penny. 

(4)  If  a  child  is  spoilt,  he  is  sure  to  be  troublesome. 

(5)  If  this  is  true,  you  are  mistaken. 

(6)  If  any  violet  is  white,  it  is  fragrant. 

(7)  If  he  told  you  anything,  it  is  true. 

(8)  If  Charles  i.  had  not  deserted  Strafford,  he  would  be  more 
deserving  of  sympathy. 

29.  Classify  Hypothetical  and  Conditional  Propositions,  with 
examples. 

SECTION    VI. 

30.  Define  Alternative  Frojjosition,  and  explain  in  what  sense 
the  elements  of  Alternative  Propositions  must  be 

(1)  exclusive 

(2)  unexclusive. 

31.  Draw  up  a  Table  of  Alternative  (Disjunctive)  Propositions, 
with  illustrations. 


QUESTIONS  AND  EXERCISES.  231 

SECTIONS  V.  AND  VI. 

32.  Define  and  analyse  Hypothetical,  Conditional,  and  Disjunc- 
tive (Alternative)  Propositions. 

SECTION   VII. 

33.  Discuss  the  place  and  value  of  Quantification  in  Logic. 

34.  What  objections  lie  against  the  view  that  the  predicate  of  a 
Logical  Proposition  should  be  written  as  a  Quantity  1 

35  To  what  extent  would  the  eight  propositions  which  result 
from  predicating  of  all  or  some  trains  that  they  do,  or  do  not,  stop 
at  all  or  some  stations,  coincide  with  the  eight  forms  obtamed  by 
quantifying  the  Predicates  of  the   ordinary  Class  Propositions, 

^'  ^'  ^'  ^  •  (Adapted  from  C.) 

36  Point  out  any  logical  difficulties  connected  with  the  use  of 
the  words  some,  few,  any  ;  and  discuss  the  proper  logical  significa- 
tion of  these  words. 

SECTION   VIIL 

37.  Give  a  general  account  of  the  Relations  of  Propositions,  with 
examples. 

38.  What  is  meant  when  it  is  said  that  one  proposition  is  related 
to  another? 

39.  What  conditions  are  necessary  in  order  that  we  should  con- 
nect propositions  by  the  conjunctions  and,  but,  etc.  ? 


40.  Define 


with  examples. 


SECTION   IX. 

Inference 

Immediate  Inference 
Mediate  Inference 


232 


QUESTIONS  AND  EXERCISES. 


41.  Discuss  the  meaning  and  importance  of  the  division  of 
Mediate  Inferences  into  Absolute  and  Relative. 

42.  What  is  the  distinction  between 

{a)  Immediate  and  Mediate  Inference 
{h)  Induction  and  Deduction. 

43.  Define  the  following  words — 

Equivalent 

Inference 

Eduction  ; 
and  give  some  examples  of  {a)  Equivalent  Categorematic  words 
(h)  Syncategorematic  Equivalent  words. 

SECTION   X. 

44.  Define  Immediate  Inference  {Eduction) ;  and   draw  up  a 
Table  of  the  most  important  kinds  of  Immediate  Inference. 

45.  Point  out  (1)  the  general  principles  of  all  Inference,  (2)  the 
special  principles  of  Immediate  Inference. 

(L.  shortened.) 

46.  Explain,  and  justify,  the  principal  kinds  of  Immediate  In- 
ference (Eduction). 

47.  All  crystals  are  solids. 
Some  solids  are  not  crystals. 
Some  not  crystals  are  not  solids. 
No  crystals  are  not  solids. 
Some  solids  are  crystals. 

Some  not  solids  are  not  crystals. 

All  solids  are  crystals. 
Assign  the  logical  relation,  if  any,  between  the  first  of  these  pro- 
positions and  each  of  the  others. 

(L.  slightly  altered.) 

48.  Give  as  complete  a  Table  as  you  can  of  the  principal  Imme- 
diate Inferences  which  can  be  drawn  from 

(1)  All  R  is  Q. 

(2)  No  R  is  Q. 

(3)  Some  R  is  Q. 

(4)  Some  R  is  not  Q. 


QUESTIONS  AND  EXERCISES. 


233 


49.  Give  the  Converse  of 

(1)  A  stitch  in  time  saves  nine. 

(2)  Fortune  often  sells  to  the  hasty  what  she  gives  to  those  who 
wait. 

60.  Give  the  Contrapositive  [Contraverse]  and  Converse  of  each 
of  the  following  : — 

(1)  If  any  nation  prospers  under  a  Protective  System,  its  citizens 
reject  all  arguments  in  favour  of  Free  Trade. 

(2)  If  any  nation   prospers   under   a   Protective  System,  we 
ought  to  reject  all  arguments  in  favour  of  Free  Trade. 

(C.  shortened.) 

51.  Examine  the  following  : — 

{a)  Men  are  weak  mortals  ;  therefore  weak  men  are  mortal. 
(6)  If  it  is  happy  to  be  ignorant,  it  is  miserable  to  be  wise. 

(C.  shortened.) 

52.  By  what  process  do  we  pass  from  each  of  the  following  pro- 
positions to  the  next  ? 

(1)  No  knowledge  is  useless. 

(2)  No  useless  thing  is  knowledge. 

(3)  All  knowledge  is  not  useless. 

(4)  All  knowledge  is  useful. 

(5)  What  is  not  useful  is  not  knowledge. 

(6)  What  is  useless  is  not  knowledge. 

(7)  No  knowledge  is  useless. 

(J.) 

53.  By  what  processes  can  we  infer  from  All  A  is  B  that — 

(1)  Some  B  is  A, 

(2)  All  not  B  is  not  A, 

(3)  Some  not  A  is  not  B, 

(4)  All  AC  is  B  ? 

Show  by  a  diagram  the  correctness  of  each  inference. 

(C.  shortened.) 

54.  Determine  the  Subject  and  Predicate  of  each  of  the  follow- 
ing propositions,  and  examine  how  they  can  be  logically  converted — 

(a)  The  angles  of  a  square  are  equal  to  one  another. 

(6)  James  was  John's  brother. 

(c)  Justice  and  equity  are  not  the  same. 

{d)  A  teacher  need  not  be  a  pedant. 

(0.) 


234 


QUESTIONS  AND  EXERCISES. 


55.  Give,  as  far  as  you  can,  the  Obverse,  Converse,  and  Contra- 
positive  (Contraverse)  of  the  following  Propositions  : — 

(1)  No  news  is  good  news. 

(2)  All  the  angles  of  a  triangle  are  equal  to  two  right  angles. 

(3)  All 's  well  that  ends  well. 

(4)  An  honest  miller  has  a  golden  thumb. 

(5)  P  struck  Q. 

(6)  Dick  is  stronger  than  Tom. 

(7)  Some  mistakes  are  disastrous. 

(8)  Improbable  events  happen  every  day. 

(9)  It  snows. 

(10)  All  that  glitters  is  not  gold. 

(11)  All  the  angles  of  a  triangle  are  less  than  two  right  angles. 

(12)  If  ancient  astronomers  were  right,  the  sun  goes  round  the 
earth. 

(13)  If  all  the  year  were  playing  holidays. 
To  sport  would  be  as  tedious  as  to  work. 

(14)  If  better  were  within,  better  would  come  out. 

(15)  I  care  for  nobody,  no,  not  I, 
If  nobody  cares  for  me. 

(16)  If  a  proposition  is  Categorical,  it  consists  of  Terms  and 
Copula. 

(17)  If  things  were  to  be  done  twice, 
All  would  be  wise. 

(18)  If  a  man  be  too  fortunate,  he  will  not  know  himself;  if  he 
be  too  unfortunate,  others  will  not  know  him. 

(19)  If  a  man  hath  one  true  friend,  he  hath  more  than  his 
share. 

(20)  Any  goose  is  grey  or  white. 

(21)  The  book  is  either  blue  or  green. 

(22)  Either  Honesty  is  the  best  policy,  or  Life  is  not  worth 
having. 

56.  Explain   Conversion    and    Contraposition   [Contraversion]. 
Apply  them  to  the  following  : — 
(a)  No  lamps  are  required. 

(6)  Some  unfortunate  people  do  but  meet  with  their  deserts. 
{c)  No  one  who  could  help  it  came. 

(C.) 


QUESTIONS  AND  EXERCISES. 


235 


57.  Discuss  the  formal  validity  of  the  following  arguments : — 
All  P  is  Q,  therefore  All  AP  is  AQ  ;  All  AP  is  AQ,  therefore 
Some  P  is  Q  ;  All  A  is  P  or  Q,  therefore  No  AP  is  AQ. 

(C.) 

58.  *  By  the  use  of  negative  terms,  all  propositions  may  be 
reduced  to  the  affirmative  form.' 

'  By  the  use  of  negative  propositions,  negative  terms  may  always 
be  eliminated.' 
Discuss  these  statements. 

(0.) 

59.  Leslie  Ellis  pointed  out  that,  though  a  St.  Bernard  dog  is 
certainly  a  dog,  a  small  St.  Bernard  dog  is  not  a  small  dog.  Ex- 
amine this. 

(L.  altered.) 

60.  Express  the  whole  import  of  the  Proposition,  '  Either  A  is 
B  or  C  is  D,'  in  the  form  of  a  single  Hypothetical,  and  prove  the 
adequacy  of  your  expression.  Give  the  converted  obverse  of  the 
proposition,  '  All  A  that  is  neither  B  nor  C  is  both  X  and  Y.' 

(L.) 

61.  Put,  if  you  can,  the  whole  meaning  of  a  Disjunctive  [Alter- 
native] Proposition  into  a  single  and  simple  Hypothetical,  and 
prove  your  expression  to  be  sufficient. 

(C.) 


SECTION   XI. 

62.  Classify  Incompatible  Propositions,  and  define 

{a)  Contrary 

(h)  Contradictory. 

63.  Find  the  Contradictory  of  each  of  the  following  proposi- 
tions : — 

(1)  All  S  is  all  P. 

(2)  Either  every  S  is  P  or  every  P  is  S. 

(3)  If  every  S  is  P,  then  every  P  is  S. 

(0.) 

64.  Of  two  Contrary  Propositions,  the  affirmation  of  the  one 
gives  a  right  to  deny  the  other,  but  the  denial  of  one  gives  no 
right  to  affirm  the  other.     Prove  this  with  an  example. 

(C.) 


236 


QUESTIONS  AND  EXERCISES. 


65.  Show  by  means  of  the  Sub-contrary  Propositions  that  Con- 
trary Propositions  may  both  be  false. 

(J.) 

66.  Show  why  the  following  propositions  are  not  true  Contra- 
dictories : — 

(1)  Wherever  A  is  present  B  is  present,  and  either  C  or  D  is 
also  present. 

(2)  In  some  cases  where  A  is  present,  either  B  or  C  or  D  is 
absent. 

How  must  (2)  be  amended  in  order  that  it  may  become  the 
true  Contradictory  of  (1)  ? 

(C.  shortened.) 

67.  Give   the    Contrary  and  Contradictory  of  the    following 
Propositions  : — 

(1)  If  this  bill  passes,  the  dock  labourers  will  benefit. 

(2)  If  the  sun  goes  round  the  earth,  anciont  astronomers  were 
wrong. 

(3)  If  black  is  white,  he  is  a  person  to  be  trusted. 

(4)  If  thd  earth  were  only  6000  miles  in  diameter,  it  would  be 
less  than  24,000  miles  in  circumference. 

(5)  If  any  violet  were  scarlet  it  would  be  scentless. 

(6)  If  any  goose  is  not  grey,  it  is  white. 

68.  What  Propositions  are  true,  false,  or  doubtful— 

(1)  When  A  is  false  ? 

(2)  When  E  is  false  ? 

(3)  When  I  is  false  ? 

(4)  When  0  is  false  ? 

(J.) 

69.  Prove,  by  means  of  the  Contradictory  Propositions,  that  Sub- 
contrary  Propositions  cannot  both  be  false. 

(J.) 

SECTIONS  X.  AND  XL 

70.  Write  down  the  Converse  and  Contradictory  of  each  of  the 
folio  wins:  : — 

(a)  England  expects  every  man  to  do  his  duty. 

(6)  Whenever  it  rains  I  stay  at  home. 

(c)  Any  one  of  average  intelligence  could  answer  this  question. 

(C.) 


QUESTIONS  AND  EXERCISES. 


237 


71.  Discuss  the  nature  of  the  distinction  between  Categorical 
and  Hypothetical  propositions. 

Examine  the  logical  relation  between  the  two  following  proposi- 
tions, and  inquire  whether  it  is  logically  possible  to  hold  (a)  that 
both  are  true,  {b)  that  both  are  false  : — (i)  If  volitions  are  undeter- 
mined, then  punishments  cannot  be  rightly  inflicted  ;  (ii)  If  punish- 
ments can  be  rightly  inflicted,  then  volitions  are  undetermined. 

(C.) 

72.  Classify  the  propositions  subjoined  into  the  four  following 
groups : — 

(a)  Those  which  can  be  inferred  from  (1) ; 

(b)  Those  from  which  (1)  can  be  inferred  ; 

(c)  Those  which  do  not  contradict  (1),  but  cannot  be  inferred 

from  it ; 

(d)  Those  which  contradict  (1). 

(1)  All  just  acts  are  expedient  acts. 

(2)  No  expedient  acts  are  unjust. 

(3)  No  just  acts  are  inexpedient. 

(4)  All  inexpedient  acts  are  unjust. 

(5)  Some  unjust  acts  are  inexpedient. 

(6)  No  expedient  acts  are  just. 

(7)  Some  inexpedient  acts  are  unjust. 

(8)  All  expedient  acts  are  just. 

(9)  No  inexpedient  acts  are  just. 

(10)  All  unjust  acts  are  inexpedient. 

(11)  Some  inexpedient  acts  are  just  acts. 

(12)  Some  expedient  acts  are  just. 

(13)  Some  just  acts  are  expedient. 

(14)  Some  unjust  acts  are  expedient. 

(J.) 


SECTION   XII. 

73.  Define 

{a)  Categorical  Argument 
(b)  Categorical  Syllogism. 

74.  State  and  explain  the  Canon  of  Categorical  Syllogisms. 

75.  Define  carefully,  with  examples,  the  following  words,  and 


238 


QUESTIONS  AND  EXERCISES. 


mention  any  synonyms  of  either  of  them  with  which  you  may  be 
acquainted  : — 

Same  Different 

Identical  Diverse 

Similar  Distinct. 

76.  State  and  justify  the  Rules  of  Categorical  Syllogism. 

77.  State  and  explain  the  Dictum  de  omni  et  nullo.  What  is 
its  place  and  value  in  inference  ? 

78.  How  is  it  that  when  M  is  predicate  in  both  the  premisses  of 
a  [Class]  SyUogism,  the  Major  Premiss  of  the  Syllogism  must  be 
universal.  /q  \ 

79.  '  Two  negative  propositions  prove  nothing.'    Why  not  ? 
Examine  the  following  : — 

No  perfect  result  was  recorded  ; 
Professor  A.'s  results  were  not  imperfect ; 
It  must,  therefore,  be  a  fact  that  Professor  A.'s  results  are  not 
recorded.  /q  \ 

80.  Supply  premisses  to  the  following  conclusions  :— 

(1)  Some  logicians  are  not  good  reasoners. 

(2)  The  rings  of  Saturn  are  material  bodies. 

(3)  Party  government  exists  in  every  democracy. 

(4)  All  fixed  stars  obey  the  law  of  gravitation, 

(J.) 

81.  Exhibit  the  following  arguments  in  logical  form,  and  test 
their  validity  by  the  rules  of  Syllogism  :— 

(a)  Where  ignorance  is  bliss,  'tis  folly  to  be  wise. 

(6)  If  those  who  mean  nobly  act  nobly,  all  heroes  must  be  men 
of  lofty  aspirations. 

(c)  None  but  the  contented  are  happy,  none  but  the  virtuous 
are  contented,  none  but  the  wise  are  virtuous,  therefore  none  but 
the  wise  are  happy. 

{d)  Queen  Victoria  is  the  mother  of  the  Duke  of  Edinburgh, 
the  Duke  of  Kent  is  the  father  of  Queen  Victoria,  therefore  tlie 
Duke  of  Kent  is  the  grandfather  of  the  Duke  of  Edinburgh. 

(C.) 


QUESTIONS  AND  EXERCISES. 


239 


82.  Put  the  following  arguments  in  logical  form,  and  consider 
their  value  : — 

(1)  He  must  have  been  the  thief,  for  he  ran  away  when  they 
called  for  the  police. 

(2)  The  study  of  grammar  is  useless  ;  for  some  men  write  gram- 
matically without  it,  and  others  write  ungrammatically  in  spite  of  it. 

(3)  This  cloth  is  too  cheap  to  be  good. 

(0.  slightly  altered.) 

83.  '  No  wise  man  is  unhappy  ;  for  no  dishonest  man  is  wise, 
and  no  honest  man  is  unhappy.'  Examine  this  inference,  and,  if 
vou  think  it  sound,  resolve  it  into  a  regular  syllogism. 

(L.) 

84.  If  it  be  known  concerning  a  [Categorical]  Syllogism  that  the 

Middle  Term  is  twice  Universal,  what  do  you  know  concerning 

the  conclusion  ]     Prove  your  answer. 

(L.) 

85.  Take  the  premisses  of  an  ordinary  Syllogism  in  Barbara, 

such  as 

All  X's  are  Y's, 

All  Y's  are  Z's. 

Determine  precisely  and  exhaustively  what  those  propositions 
affirm,  what  they  deny,  and  what  they  leave  in  doubt,  concerning 

the  relations  of  the  Terms  X,  Y,  and  Z. 

(L.) 

86.  What  do  you  understand  by  Mood  and  Figure  in  Syllo- 
gism? 

87.  Explain  the  terms  Figure  and  Eediidion  as  applied  to  the 

Syllogism. 

Find  what  connection  between  Philosophers  and  Illiterate  Per- 
sons can  be  syllogistically  concluded  from  each  of  the  following  :— 

(1)  B,  though  an  illiterate  person,  was  a  philosopher. 

(2)  Some  illiterate  persons,   but  no  philosophers,  use   strong 

language. 

Give  in  each  case  the  mood  and  figure  of  the  syllogism^  and 
show  how  it  may  be  reduced  to  the  first  Figure. 

(C.) 


240 


QUESTIONS  AND  EXERCISES. 


88.  Express  by  means  of  ordinary  Categorical  Propositions  the 
relation  between  S  and  P  represented  by  the  following  diagram  : — 


Represent  Celarent  by  the  aid  of  Euler's  diagrams.    Will  the  same 
set  of  diagrams  serve  for  any  other  of  the  syllogistic  moods  ? 

(C.  shortened.) 

89.  Show  (a)  that  the  following  moods  are  invalid  in  any  figure  : 

AIA,  EEI,  lEA,  lOI,  IIA,  AEI  ; 

b)  in  what  figures  the  following  premisses  give  a  valid  conclusion  : 

AA,  AI,  EA,  OA  ; 

(c)  in  what  figures  lEO  and  EIO  are  valid. 

(Adapted  from  J.) 

90.  To  what  moods  do  the  following  valid  syllogisms  belong  ? 
Arrange  them  in  correct  logical  order. 

(1)  Some  Y's  are  Z's, 
No  X's  are  Y's, 
Some  Z's  are  not  X's. 

(2)  All  Z's  are  Y's, 
No  Y's  are  X's, 
No  Z's  are  X's. 

(J.  shortened.) 

91.  Deduce  conclusions  from  the  following  premisses,  and  state 
to  what  mood  the  syllogism  belongs  : — 

(1)  Some  amphibia  are  mammalian  ; 
All  mammalians  are  vertebrate. 

(2)  All  planets  are  heavenly  bodies  ; 
No  planets  are  self-luminous. 

(3)  Mammalians  are  quadrupeds  ; 
No  birds  are  quadrupeds. 

(4)  Ruminants  are  not  predacious  ; 
The  lion  is  predacious. 

(J.) 


QUESTIONS  AND  EXERCISES. 


241 


92.  Prove,  generally,  without  reference  to  particular  moods,  that 
in  the  third  Figure  the  Minor  Premiss  must  be  affirmative  and  the 
conclusion  particular,  and  that  the  second  Figure  can  prove  only 
negatives. 

Examine  the  argument :  *  You  cannot  be  right  in  denying  that 
any  of  the  killed  were  English,  considering  that  none  but  English 
were  in  camp,  and  none  but  those  in  camp  were  killed.' 

(0.) 

93.  Which  kind  of  proposition  cannot  become  a  premiss  in  the 
first  Figure,  and  why  not  ? 

(0.) 

94.  For  what  reasons  must  an  affirmative  major  premiss  be  fol- 
lowed by  an  affirmative  minor  premiss  in  the  first  and  third 
figures,  by  a  negative  minor  in  the  second,  and  by  a  universal 
minor  in  the  fourth  ? 

(0.) 

95.  Why  cannot  0  stand  as  a  Premiss  in  the  first  Figure,  as 
Major  in  the  Third,  or  as  a  Premiss  in  the  fourth  ? 

(0.  shortened.) 

96.  If  it  be  known  concerning  a  Class-syllogism  that  the  Middle 
Term  is  distributed  in  both  premisses,  what  can  we  infer  as  to  the 
conclusion  ? 

(C.  slightly  changed.) 

97.  Prove  that  the  third  Figure  must  have  an  affirmative  Minor 
Premiss,  and  a  Particular  Conclusion. 

(J.) 

98.  Reduce  the  moods  Cesare  and  Camenes  by  the  Indirect 
Method,  or  lieductio  ad  Iinjiossihile. 

(J.) 

99.  Write  out  a  Syllogism  in  each  of  the  Four  Figures. 

100.  Why  must  the  conclusion  in  Fig.  2  be  negative,  and  the 
conclusion  in  Fig.  3  particular  ? 

101.  Construct  Syllogisms  in  Baroko  and  Camenes,  and  reduce 
them  to  Fig.  1. 

102.  Reduce  Bokardo  both  directly  and  indirectly. 

Q 


242 


QUESTIONS  AND  EXERCISES. 


103.  Reduce  Barbara  to  Celarent,  Darii,  and  Ferio. 

104.  What  is  meant  by  an  argument  a  fortioril  Give  an 
example,  and  show  the  exact  logical  foundation  of  the  reasoning. 

(C.) 

105.  State  the  Canon  of  Relative  Categorical  Arguments,  and 
explain  why  it  is  not  more  precise. 

SECTION    XIII. 

106.  Take  an  instance  of  an  Inductive  Generalisation  (not 
mathematical),  and  set  out  at  full  length  the  reasonings  and 
assumptions  which  it  involves. 

107.  State  and  explain  the  Inductive  Principle  of  Interdepend- 
ence. 

108.  It  is  maintained,  on  the  one  hand,  tliat  no  inference  is 
valid  in  which  the  conclusion  is  not  contained  in  the  premisses ; 
and,  on  the  other  hand,  that  no  movement  of  thought  deserves  to 
be  entitled  Inference  in  which  there  is  not  progress  from  the 
known  to  the  unknown.  Examine  the  grounds  for  the  two  state- 
ments, and  discuss  the  possibility  of  holding  them  jointly. 

(L.) 

109.  Distinguish  between  Inference  and  Conjecture.  How  do 
the  Premisses  of  an  Inductive  Inference  differ  from  those  of  a 
Deductive  ? 

'  The  wind  has  gone  round  to  the  west,  and  we  shall  have  rain.' 
Analyse  fully  the  logical  processes  involved  in  this  assertion. 

(C.) 

1 10.  '  In  one  instance  AB  is  followed  by  XY  ;  in  another,  AC 
is  followed  by  XZ.'  Show  concisely  what  general  postulates,  and 
what  special  conditions,  are  required  to  justify  each  of  the  follow- 
ing inferences  from  the  above  : — 

(1)  Every  A  is  followed  by  an  X  ; 

(2)  Every  B  is  followed  by  a  Y  ; 

(3)  Every  X  is  preceded  by  an  A  ; 

(4)  Every  Y  is  preceded  by  a  B. 

(C.) 


/ 


QUESTIONS  AND  EXERCISES. 


243 


111.  If  any  one  told  you  that  he  saw  a  ghost  last  night,  what 
grounds  would  you  have  for  disbelieving  him,  and  what  ought  to 
be  the  limits  of  your  incredulity  ? 

(C.) 

112.  When  two  phenomena  are  causally  connected  together,  can 
you  always  ascertain  which  is  the  cause  and  which  is  the  effect  ? 
If  so,  how  ? 

(L.) 

113.  Explain  the  terms  LaWy  Uniformity ^  Cause. 
Examine  into  the  use  of  the  word  Cause  in  the  following  : — 
{a)  The  cause  of  his  mistake  was  ignorance. 

(6)  The  cause  of  the  fall  of  a  stone  is  the  universal  law  of  gravi- 
tation. 

(C.) 

114.  Can  you  account  for  the  unique  character  of  Mathematical 
Generalisations  ? 

115.  What  is  the  general  nature  of  an  argument  from  Analogy  1 
How  do  you  distinguish  Analogy  from  Metaphor  and  Example  ? 

(C.) 

116.  Set  out  at  length  an  instance  of  an  Inductive  Argument 
by  Analogy. 

117.  Distinguish  between  Induction,  Analogy,  and  Example. 
Of  what  kind  are  the  following  arguments,  and  why  ? 

(a)  If  a  stone  breaks  the  window,  so  will  a  cricket-ball ; 

(6)  If  one  penny  turns  greenish  when  dipped  in  vinegar,  so  will 
all  pennies  ; 

(c)  If  birds  of  a  feather  flock  together,  so  will  men  of  the  same 
trade. 

(C.) 

118.  Define  Hypothesis,  and  give  some  tests  for  judging  the 
value  of  a  Hypothesis. 

(C.) 

119.  Describe  the  methods  which  might  be  used  to  establish  the 
following  laws  : — 

'  Bodies  expand  under  the  action  of  heat.' 
^  Commerce  is  benefited  by  free  trade.' 

(C.) 


244 


QUESTIONS  AND  EXERCISES. 


120.  Discuss  the  value  of  the  Method  of  Agreement  and  the 
Method  of  Difference,  contrasting  them  as  to  the  possibility  of 
applying  them,  and  their  conclusiveness  when  applied. 

(C.) 

121.  Analyse  briefly  the  logical  methods  by  which  are  estab- 
lished— 

(a)  the  Law  of  Universal  Gravitation  ; 
(h)  the  Parallelogram  of  Forces  ; 

(c)  the  proposition  that  the  three  angles  of  every  triangle  are 
together  equal  to  two  right  angles. 

(C.) 

122.  By  what  logical  methods  would  you  test  the  following  pro- 
positions : — 

(a)  Air  has  weight. 

(6)  A  moving  body,  unless  interfered  with,  never  changes  its 
direction  or  velocity. 

(c)  Free  trade  conduces  to  national  prosperity. 

(d)  In  social  development,  the  military  precedes  the  industrial 
state. 

(C.) 

123.  Which  of  the  Inductive  Methods  is  best  adapted  to  scien- 
tific inquiry  in  the  cases  where  experiment  is  impossible  ? 

(C.  shortened.) 

124.  Enumerate  and  explain,  with  illustrations,  the  so-called 
Methods  of  Induction,  and  point  out  their  precise  place  and  value 
in  Logic. 

125.  Write  down  the  definitions,  axioms,  and  postulates  in- 
volved in  proving  the  causal  dependence  of  phenomena  by  the 
Method  of  Agreement. 

(C.) 

126.  Explain  what  is  meant  by  the  Joint  Method  of  Agreement 
and  Difference  ;  and  point  out  wherein  it  differs  from  the  Simple 
Method  of  Difference. 

(C.) 

127.  Why  is  a  single  instance  sometimes  sufficient  to  warrant 
an  universal  conclusion,  while  in  other  cases  the  greatest  possible 


QUESTIONS  AND  EXERCISES. 


245 


number  of  concurring  instances,  without  any  exception,  is  not 
sufficient  to  warrant  such  a  conclusion  ? 

(J.) 

128.  What  can  you  infer  from  the  following  instances  ? 
Antecedents.                                                     Consequents. 
ABDE stqp. 


BCD 

BFG 

ADE 

BHK 

ABFG 

ABE 


qsr. 

vqu. 

tsp. 

zqw. 

pquv. 

pqt. 


(J.) 


129.  Supposing  us  to  be  unacquainted  with  the  causes  of  the 
following  phenomena,  by  what  method  should  we  investigate  each  ? 

(1)  The  connection  between  the  barometer  and  the  weather. 

(2)  A  person  poisoned  at  a  meal. 

(3)  The  connection  between  the  hands  of  a  clock. 

(4)  The  effect  of  the  Gulf  Stream  upon  the  climate  of  Great 
Britain. 

(J.) 

130.  Draw  up  a  list  of  the  Experimental  Methods,  in  what  you 
consider  to  be  the  order  of  their  cogency.  Give  reasons  for  your 
arrangement  of  them,  and  show  that  they  are  all  'reducible  to  two 
only,  the  Method  of  Agreement  and  the  Method  of  Difference.' 

(C.) 


SECTION   XIV. 

131.  Define  and  divide  Inferential  Mediate  Inference. 

132.  Discuss  the  nature  of  the  reasoning  contained,  or  ap- 
parently intended,  in  the  following  sentences  : — 

(a)  It  is  impossible  to  prove  that  persecution  is  justifiable  if 
you  can't  prove  that  some  non-effective  measures  are  justifiable, 
for  no  persecution  has  ever  been  effective. 

(b)  This  deed  may  be  genuine  though  it  is  not  stamped,  for 
some  unstamped  deeds  are  genuine. 

(C. 


246 


QUESTIONS  AND  EXERCISES. 


133.  Examine  the  following  arguments  : — 

(i)  If  the  earth  turns  on  its  axis,  falling  bodies  must  diverge 
from  the  perpendicular ;  now,  experiment  shows  that  they  do  so 
diverge,  therefore  the  earth  must  turn  on  its  axis. 

(ii)  How  can  you  admit  that  any  wise  men  are  unhappy,  when 
you  deny  that  any  dishonest  men  are  wise,  and  also  that  any 
honest  men  are  unhappy  ? 

(C.) 


SECTION    XV. 

134.  Define  Alternative  (or  Disjunctive)  Mediate  Inference. 

135.  What  is  the  Canon  of  Pure  Alternative  Arguments  ? 

136.  Arrange  in  logical  form  the  following  argument : — 
Compulsory  legislation  against  intemperance  is  to  be  avoided  ; 

for  it  is  mischievous  if  obeyed  unwillingly,  and  useless  if  obeyed 
willingly. 

(C.) 

137.  '  If  X  is  true,  then  either  Y  or  Z  is  true  ;  but  Y  is  not 
true.'    What  conclusion  can  be  drawn  ? 

(C.  shortened.) 

SECTION   XVI. 

138.  Discuss  briefly  the  characteristics  of  a  satisfactory  Method 
of  Science. 

139.  Enumerate  the  rules  for  a  sound  Division,  and  the  requi- 
sites for  a  good  Classification.  Is  there  any  connection  between 
the  Principles  of  Division  and  those  of  Classification  ? 

(C.) 

140.  Divide  any  of  the  follow  ing  classes  ; — 

Governments, 
Sciences, 
Logical  Terms, 
Propositions. 

(J.) 


QUESTIONS  AND  EXERCISES. 


247 


141.  What  is  meant  by  Cross  Division  and  the  fundamentiim 
divisionis  1    Illustrate  by  giving  a  classification  of  Games. 

(C.) 

142.  Criticise  the  following  Divisions  : — 

(1)  Great  Britain  into  England,  Scotland,  Wales,  and  Ireland. 

(2)  Pictures  into  sacred,  historical,  landscape,  and  mythological. 

(3)  Vertebrate  Animals    into    quadrupeds,  birds,  fishes,  and 
reptiles. 

(4)  Plant  into  stem,  root,  and  branches. 

(5)  Ship  into  frigate,  brig,  schooner,  and  merchantman. 

(6)  Books  into  octavo,  quarto,  green  and  blue. 

(7)  Figures  into  curvilinear  and  rectilinear. 

(8)  Ends  into  those  which  are  ends  only,  means  and  ends,  and 
means  only. 

(9)  Church  into  Gothic,  Episcopal,  High,  and  Low. 

(10)  Sciences  into  physical,  moral,  metaphysical,  and  medical. 

(11)  Library  into  public  and  private. 

(12)  Horses  into  racehorses,  hunters,  hacks,  thoroughbreds, 
ponies,  and  mules. 

(Stock,  Deductive  Logic.) 

143.  The  first  name  in  each  of  the  following  series  of  terms  is 
that  of  a  class  which  you  are  to  divide  and  subdivide  so  as  to 
include  all  the  subjoined  minor  classes  in  accordance  with  the 
laws  of  Division  : — 

(1)  People. 

Laity.  Natural-born  Subjects. 

Aliens.  Clergy. 

Naturalised  Subjects.  Baronets. 


Peers. 

Equiangular, 

Isosceles. 

Right-angled. 

Induction. 
Deduction. 
Mediate  Inference. 


Commons. 
(2)  Triangle. 

Scalene. 


Obtuse-angled. 


(3)  Beasoning. 

Hypothetical  Syllogism. 
Disjunctive  Syllogism. 


(J.) 


248 


QUESTIONS  AND  EXERCISES. 


144.  Distinguish  between — 

Classing, 
Classification, 
Systematisation  ; 
and  discuss  the  relation  between  Division  and  Classification. 

145.  Explain  the  main  objects  aimed  at  in  a  scientific  classifica- 
tion. 

(0.) 

146.  Suggest  principles  on  which  a  classification 

(1)  of  the  Sciences, 

(2)  of  Athletic  Games, 

might  be  based  ;  and  illustrate  your  suggestions  by  drawing  up  a 
scheme  of  classification  of  (1)  or  (2). 

SECTION    XVII. 

147.  What  do  you  understand  by  the  Definition  of  a  word? 
How  is  Signification  determined  ? 

148.  Discuss  the  relation  between — 

(a)  Definition  and  Classing, 
(6)  Classing  and  Induction. 

149.  Discuss  some  of  the  sources  of  ambiguity  in  language  ;  and 
point  out  the  varying  importance,  in  difl'erent  cases,  of  a  reference 
to  context. 

150.  Distinguish  the  difl'erent  objects  aimed  at  in  definition  ; 
and  consider  how  the  method  and  rules  of  definition  will  vary 
according  to  the  object  primarily  had  in  view. 

(C.) 

151.  What  are  the  principal  faults  to  be  avoided  in  a  defini- 
tion ?  Illustrate  them  by  definitions  of  ^Athletics'  and  *  Examina- 
tions.' 

(C.) 

152.  What  are  the  objections  to  the  following  definitions  ? 

(a)  A  table  is  a  wooden  article  of  furniture  not  intended  to  be 
sat  upon. 

(6)  Barbarism  is  the  name  given  to  the  condition  of  such  coun- 
tries as  Patagonia,  the  Feejee  Islands,  etc. 

(C.  shortened.) 


QUESTIONS  AND  EXERCISES. 


249 


153.  When  is  Definition  serviceable  for  recognition  ? 

154.  Criticise  the  following  definitions  : — 

(1)  A  barometer  is  a  thing  that  you  tap  in  the  hall,  and  grunt. 

(2)  An  albatross  is  a  bird  known  to  the  readers  of  Coleridge's 
Ancient  Mariner. 

(3)  A  net  is  a  reticulated  fabric,  decussated  at  regular  intervals. 

(4)  An  Archdeacon  is  a  person  who  performs  archi-diaconal 
functions . 

(5)  An  acute-angled  triangle  is  a  triangle  which  has  one  acute 
angle. 

(6)  A  geranium  is  a  scarlet  flower. 

(7)  The  dog  is  the  friend  of  man. 

(8)  Selfishness  is  the  bane  of  Society. 

(9)  A  circle  is  a  plane  figure  contained  by  one  line. 

(10)  A  triangle  is  a  figure  contained  by  three  straight  lines  of 
equal  length. 

155.  What  are  the  requisites  for  the  full  equipment  of  a  lan- 
guage for  scientific  purposes  ? 

(0.) 

156.  What  are  the  chief  tendencies  at  work  in  altering  the 


meaning  of  names  ?     Illustrate  them. 


(0.) 


157.  To  what  extent  is  Definition  an  arhitranj  Process  ?  Illus- 
trate by  reference  to  definitions  in  Natural  History  and  Political 

Economy. 

(C.) 

158.  Explain  what  is  the  logical  ideal  of  language  regarded  as 
an  instrument  of  thought  ;  and  show  why  this  ideal  is  practically 
unattainable. 

Under  what  conditions,  and  within  what  limits,  is  it  legitimate 
to  employ  an  old  word  with  a  new  meaning  ? 

(C.) 


SECTION   XVIII. 

159.  Define  Fallacy ^  with  examples. 

160.  Give  a  classification  of  Fallacies. 


250 


QUESTIONS  AXD  EXERCISES. 


Examine  the  ambiguities  in  the  following  : — 
(a)  He  likes  work  and  athletics  very  much. 
(h)  How  much  is  5  added  to  3  squared  ? 

How  are  such  ambiguities  as  the  above  avoided  by  mathe- 
matical notation  ? 

(C.) 

161.  Examine  the  following  arguments.  Where  they  are  valid, 
reduce  them  to  syllogistic  form  ;  and  where  they  are  invalid, 
explain  the  nature  of  the  fallacy  : — 

(a)  His  cowardice  might  have  been  inferred  from  his  cruelty  ; 
for  all  cowards  are  cruel. 

(0)  None  but  members  of  the  University  are  present ;  all  who 
are  present  are  members  of  the  Union  ;  therefore  all  members  of 
the  Union  are  members  of  the  University. 

(c)  No  unjust  man  is  happy  ;  for  all  wise  men  are  just,  and  no 
man  who  lacks  wisdom  is  happy. 

(C.) 

162.  Examine  the  followinir : — 

You  do  not  know  what  I  am  going  to  ask  you  about.  Now  I 
am  going  to  ask  you  about  the  nature  of  the  fallacy  called  Igno- 
ratio  Elenchi.  It  seems,  therefore,  that  you  do  not  know  the 
nature  of  the  fallacy  called  Ljnomtio  Elenchi. 

(Shortened  from  C.) 

163.  Examine  the  folio wincf : — 

(1)  Governments  are  good  which  promote  prosperity  ; 

The  government  of  Burmah  does  not  promote  prosperity  ; 
Therefore  it  is  not  a  good  government. 

(2)  Land  is  not  property  ; 
Land  produces  barley ; 
.'.  Beer  is  intoxicating. 

(3)  Nothing  is  property  but  that  which  is  the  product  of  man's 
hand ; 

The  horse  is  not  the  product  of  man's  hand  ; 
.'.  The  horse  is  not  property. 

(4)  Saturn  is  visible  from  the  earth,  and  the  moon  is  visible 
from  the  earth  ; 

.*.  The  moon  is  visible  from  Saturn. 

(5)  Sparing  the  rod  spoils  the  child  ;  so  John  will  turn  out  very 
good,  for  his  mother  beats  him  every  day. 


QUESTIONS  AND  EXERCISES. 


251 


(6)  Socrates  was  wise,  and  wise  men  alone  are  happy  ; 
Therefore  Socrates  was  happy. 

(Adapted  from  Stock,  Deductive  Logic.) 

164.  Persons,  it  is  said,  acquire  wisdom  by  experience.  Indicate 
clearly  the  logical  and  extra-logical  operations  involved  in  the  pro- 
cess. Show  to  what  kinds  of  error  the  following  popular  proverbs 
point : — 

All  is  not  gold  that  glitters. 

Do  not  count  your  chickens  before  they  are  hatched. 

A  man  is  not  a  horse  because  he  is  born  in  a  stable. 

A  bad  workman  complains  of  his  tools. 

Happy  is  the  bride  the  sun  shines  on. 

(C.  slightly  altered.) 

165.  Them  or  thir  feythers,  thou  sees,  mun  'a  beiin  a  laazy  lot, 
For  work  mun  'a  gone  to  the  gittin',  whiniver  munny  was 

got. 
Examine  the  validity  of  the  argument  implied  in  the  above. 

166.  Examine  the  following  arguments  : — 

(a)  If  an  import  duty  affords  Protection,  it  is  mischievous  ; 

This  import  duty  is  mischievous  ; 

Therefore  it  affords  Protection. 
(6)  Ironmongers  sell  penknives  ; 

This  man  has  sold  a  penknife  ; 

Therefore  he  is  an  ironmonger, 
(c)  A  is  B  or  C  ; 

AisC; 

Therefore  A  is  not  B. 

167.  Write  a  brief  essay  on  the  forms  of  Fallacy  most  usually 
found  in  writing  and  speaking. 

(C.) 


SECTIONS  XII.,  XIV.,   XV.,   XVIIL 

168.  Examine  the  following  arguments  : — 

(1)  Rain  has  fallen  if  the  ground  is  wet ;  but  the  ground  is  not 
wet ;  therefore  rain  has  not  fallen. 

(2)  If  rain  has  fallen,  the  ground  is  wet ;  but  rain  has  not  fallen  ; 
therefore  the  ground  is  not  wet. 


252 


QUESTIONS  AND  EXERCISES. 


(3)  The  ground  is  wet  if  rain  has  fallen  ;  the  ground  is  wet ; 
therefore  rain  has  fallen. 

(4)  If  the  ground  is  wet,  rain  has  fallen  ;  but  rain  has  fallen ; 
therefore  the  ground  is  wet. 

(5)  Cogito ;  ergo,  sum. 

(6)  Blessed  are  the  merciful ;  for  they  shall  obtain  mercy. 

(7)  Every  candid  man  acknowledges  merit  in  a  rival ;  every 
learned  man  does  not  do  so  ;  therefore  every  learned  man  is  not 
candid. 

(8)  If  pain  is  severe,  it  will  be  brief ;  and  if  it  last  long  it  will 
be  slight ;  therefore  it  is  to  be  patiently  borne. 

(9)  Elementary  substances  alone  are  metals  ;  Iron  is  a  metal  ; 
therefore  iron  is  an  elementary  substance. 

(10)  Nothing  is  better  than  wisdom  ;  dry  bread  is  better  than 
nothing  ;  therefore  dry  bread  is  better  than  wisdom. 

(11)  His  imbecility  of  character  might  have  been  inferred  from 
his  proneness  to  favourites ;  for  all  weak  princes  have  this 
failing. 

(12)  Every  one  desires  virtue,  because  every  one  desires  happi- 
ness. 

(13)  Books  are  a  source  both  of  instruction  and  amusement ;  a 
table  of  logarithms  is  a  book  ;  therefore  it  is  a  source  of  both  in- 
struction and  amusement. 

(14)  You  are  not  what  I  am  ;  I  am  a  man  ;  therefore  you  are 
not  a  man. 

(15)  Gold  and  silver  are  wealth  ;  and  therefore  the  diminution 
of  the  gold  and  silver  in  the  country  by  exportation  is  the  diminu- 
tion of  the  wealth  of  the  country. 

(16)  Night  must  be  the  cause  of  day  :  for  it  invariably  pre- 
cedes it. 

(17)  All  presuming  men  are  contemptible  ;  this  man,  therefore, 
is  contemptible  ;  for  he  presumes  to  believe  that  his  opinions  are 
correct. 

(18)  Who  is  most  hungry  eats  most;  who  eats  least  is  most 
hungry  ;  therefore  who  eats  least,  eats  most. 

(19)  Honesty  deserves  reward  ;  and  a  negro  is  a  fellow- creature ; 
therefore  an  honest  negro  is  a  fellow-creature  deserving  of  reward. 

(20)  A  man  that  hath  no  virtue  in  himself  ever  envieth  virtue 
in  others  ;  for  men's  minds  will  either  feed  upon  their  own  good 


QUESTIONS  AND  EXERCISES. 


253 


or  upon  other's  evil ;  and  who  wanteth  the  one  w  ill  prey  upon  the 
other. 

(21)  The  scarlet  poppy  belongs  to  the  genus  Papaver,  of  the 
natural  order  Papaveracese  ;  which,  again,  is  part  of  the  sub-class 
Thalamiflorae,  belonging  to  the  great  class  of  Dicotyledons.  Hence 
the  scarlet  poppy  is  one  of  the  Dicotyledons. 

(22)  Improbable  events  happen  almost  every  day  ;  but  what 
happens  almost  every  day  is  a  very  probable  event  ;  therefore 
improbable  events  are  very  probable  events. 

(23)  Elephants  are  stronger  than  horses  ;  horses  are  stronger 
than  men  ;  therefore  elephants  are  stronger  than  men. 

(24)  Alexander  was  the  son  of  Philip  ;  therefore  Philip  was  the 
father  of  Alexander. 

(25)  Nay,  look  you,  I  know  'tis  true  ;  for  his  father  built  a 
chimney  in  my  father's  house,  and  the  bricks  are  alive  at  this  day 
to  testify  to  it. 

(26)  It  is  probable  that  Herodotus  recorded  only  what  he  heard 
concerning  Ethiopia  ;  and  it  is  not  unlikely  that  most  of  what  he 
heard  was  correct ;  so  that  we  may  accept  his  account  as  true. 

(27)  In  defending  a  prisoner,  his  counsel  must  either  deny  that 
the  deed  committed  is  a  crime,  or  he  must  deny  that  the  prisoner 
committed  the  deed  ;  therefore,  if  the  counsel  denies  that  the  deed 
committed  is  a  crime,  he  must  admit  that  the  prisoner  did  commit 
the  deed. 

(28)  '  I  will  go  on,'  said  King  James.  *  I  have  been  only  too 
indulgent.     Indulgence  ruined  my  father.' 

(29)  A  magnitude  required  for  the  solution  of  a  problem  must 
satisfy  a  particular  equation  ;  and  as  the  magnitude  X  satisfies  this 
equation,  it  is  therefore  the  magnitude  required. 

(30)  If  we  never  find  skins  except  as  the  teguments  of  animals, 
we  may  safely  conclude  that  animals  cannot  exist  without  skins. 
If  colour  cannot  exist  by  itself,  it  follows  that  neither  can  anything 
that  is  coloured  exist  without  colour.  So,  if  language  without 
thought  is  unreal,  thought  without  language  must  also  be  unreal. 

(From  J.) 

SECTION   XIX. 

169.  Discuss  the  meaning  and  implications  of  the  Law  of 
Identity  in  Diversity. 


254 


QUESTIONS  AND  EXERCISES. 


170.  Consider  the  relations  between  the  Laws  of— 

(a)  Identity  in  Diversity, 

(b)  Contradiction, 

(c)  Excluded  Middle. 

171.  Examine  the  Inductive  Principle  of  Interdependence. 

172.  What   are   the   assumptions   on   which  Mill's   Inductive 
Methods  are  based  ? 

173.  Consider  the  importance  in  Logic   of  the  Principle   of 
Identity  in  Diversity. 

174.  State  the  Principles  of  Relative  Inference  and  the  Principle 
of  Self-evidence. 

175.  Show  how  the  principal  Categories  of  Logic  come  under 
the  head  of  Lenity  in  Difference. 

MISCELLANEOUS. 

176.  An  unintelligent  person  is  popularly  said  to  be  incapable 
of  putting  two  ideas  together.  Examine  this  statement,  and  illus- 
trate by  it  the  subject-matter  of  logical  inquiry. 

(C.) 

177.  State  the  precise  character,  and  give  a  complete  analysis 
of  the  logical  procedure  adopted  by  Euclid  in  demonstrating  the 
proposition  :  '  Upon  the  same  base,  and  on  the  same  side  of  it, 
there  cannot  be  two  triangles  that  have  their  sides  which  are 
terminated  in  one  extremity  of  the  base  equal  to  one  another,  and 
likewise  those  which  are  terminated  in  the  other  extremity.' 

(C.) 

178.  Show  the  precise  value  and  character  of  historical  evidence. 

(C.) 

179.  Show  the  precise  character  and  value  of  statistical  evidence. 

(C.) 

180.  Give  a  logical  analysis  of  Euclid's  method  of  finding  the 
centre  of  a  circle. 

(C.) 

181.  What  is  meant  by  the  distrihution  of  terms  in  a  propo- 
sition ?      Explain   why   from    the    proposition,    'All    equilateral 


QUESTIONS  AND  EXERCISES. 


255 


V 


triangles  are  equiangular,'  we  cannot  infer,  'All  equiangular 
triangles  are  equilateral ' ;  but  from  '  No  parallel  lines  meet,'  we 
may  infer,  '  No  lines  which  meet  are  parallel.' 

(C.) 

182.  State  the  precise  character,  and  give  a  complete  analysis  of 
the  logical  procedure  adopted  by  Euclid  in  demonstrating  the  pro- 
position, '  If  two  angles  of  a  triangle  be  equal  to  each  other,  the 
sides  also  which  are  opposite  to  the  equal  angles  shall  be  equal  to 
each  other.' 


(C.) 


183.  Describe  the  methods  of  reasoning  known  as — 
ia)  Indudlo  i^er  enumerationem  simplicem^ 
(6)  Analogy. 


(C.) 


184.  What  difference  of  meaning  would  you  assign  to  the  terms 
Sophism,  Fallacy,  Paralogism,  and  Paradox  ?  Explain  precisely 
what  is  meant  by  Petitio  Principii. 

(L.) 

185.  Construct  a  Tree  of  Porphyry y  illustrating  by  it,  as  far  as 
you  can,  the  Predicables,  Division  and  Definition  ;  and  take  Infer- 
ence for  your  Summum  Genus,  and  Bohardo  for  your   Infima 

Species. 

186.  Explain  and  illustrate  what  is  meant  by  Perfect  Induction. 
Give  and  discuss  reasons  for  and  against  the  view  that  Perfect 
Induction  is  improperly  called  Induction.     {Cf.  Note  iii.) 

(C.) 

187.  '  As  often  as  the  same  circumstances  are  repeated  the  same 
effect  will  follow,  yet  where  the  effect  is  the  same  we  cannot  infer 
that  the  cause  is  the  same  too.'  Explain  this  statement  fully, 
taking  especial  account  of  the  meaning  to  be  given  to  same. 

(L.) 

188.  Gessante  causa  cessat  et  effectus.  Discuss  this  doctrine,  and 
consider  whether  the  cases  in  which  it  appears  true,  and  the  cases 
in  which  it  does  not,  have  each  some  other  distinguishing  charac- 
teristic by  which  this  difference  might  be  explained. 

(L.) 


^it^!:£ 


256 


QUESTIONS  AND  EXERCISES. 


189.  Explain— 

(1)  Dictum  de  omni  et  niillo. 

(2)  Illicit  Process  of  the  Major. 

(3)  Undistributed  Middle. 

(4)  Reduction. 
Why  are 

AEE,  OAO,  AOO, 

invalid  moods  in  Fig.  1  ? 

Explain  and  illustrate  by  original  examples  the  use  of  the 
mnemonic  letters  in 

Camestres, 

Bokardo, 

Baroko. 

(C.  slightly  altered.) 

190.  Describe  the  process  of  Mediate  Inference,  and  give  the 
rules  for  testing  its  validity.  Show  clearly  why  the  first  and  third 
figures  of  the  Syllogism  require  the  minor  premiss  to  be  affirma- 
tive, and  why  the  second  figure  must  have  a  negative  conclusion. 

(C.  slightly  altered.) 

191.  Describe  the  Methods  of  Agreement  and  Difference,  indi- 
cating the  nature  and  degree  of  cogency  of  each.  Why  may  they 
be  called  Methods  of  Elimination  ?  Illustrate  their  application  by 
original  examples. 

(C.  slightly  altered.) 

192.  What  do  you  mean  by  saying  that  *a  phenomenon  has 
been  satisfactorily  explained '  ? 

(C.) 

193.  Construct  a  Itamean  Tree  taking  Plane  Figure  as  your 
highest  genus  ;  and  illustrate  by  reference  to  it  the  meaning 
of— 

(1)  Genus.  (4)  Infima  Species. 

(2)  Summum  Genus.  (5)  Differentia. 

(3)  Species.  (6)  Division  by  Dichotomy. 

194.  Examine  the  followinfj  arguments  : — 

(a)  Men  can  reason  without  a  knowledge  of  Logic ;  therefore 
the  study  of  Logic  is  useless. 

(6)  If  a  man  is  prudent,  he  will  not  do  evil  deliberately,  and  if 


,  I 


QUESTIONS  AND  EXERCISES. 


257 


a  man  is  strong,  he  will  not  do  evil  impulsively  ;  therefore  if  he 
does  evil,  he  must  be  either  foolish  or  weak. 

(c)  A  man  eats  either  because  he  is  hungry  or  because  he  is  fond 
of  eating  ;  hence,  if  he  eats  when  he  is  hungry,  he  is  not  fond  of 


eating. 


(C.) 


195.  How  would  you  prove,  inductively  and  deductively,  that 
Food  is  necessary  to  life  ? 

(C.) 

196.  Supply  the  assumptions,  and  examine  the  cogency,  of  the 
following  arguments  : — 

(1)  A  riot  must  have  been  apprehended  in  Mallow  last  week, 
or  they  would  not  have  sent  for  the  police. 

(2)  War  must  be  expected  ;  for  the  price  of  wheat  is  daily 
advancing. 

(C.) 

197.  Examine  the  following  arguments  : — 

(1)  Elementary  education,  being  compulsory,  ought  to  be  free. 

(2)  The  first  five  boats  are  not  allowed  to  change  their  relative 
position  ;  for  I  saw  them  come  to  the  post  six  nights  running  in 
the  same  order. 

(3)  No  one  willingly  does  wrong  ;  for  wrong-doing  certainly 
leads  to  misery,  and  no  one  desires  to  be  miserable. 

(4)  If  I  accept  the  place  offered  me,  I  shall  have  more  work  ;  if 
I  refuse  it,  I  shall  have  less  pay  ;  but  increased  work  and  inferior 
pay  are  both  evils  ;  therefore  I  had  better  neither  accept  nor 
refuse  it. 

(0.) 

198.  Examine  technically  the  following  arguments  : — 

(a)  None  but  undergraduates  were  in  the  gallery;  and  none 
but  those  in  the  gallery  could  hear ;  therefore  none  but  under- 
graduates could  hear. 

(6)  Few  Englishmen  have  any  political  knowledge  ;  all  who 
have  any  political  knowledge  should  have  the  franchise ;  there- 
fore few  Englishmen  should  have  the  franchise. 

(c)  All  ragged  persons  must  either  he  poor  or  wish  to  be  thought 
poor  :  this  ragged  person  wishes  to  be  thought  poor  ;  therefore  he 
is  not  poor.  (Q.) 

R 


ilifilBiiiiiliiii'iiMiMiiiriMiliiiliiii 


258 


QUESTIONS  AND  EXERCISES. 


199.  Distinguish  between  Experiment  and  mere  passive  Obser- 
vation.    In  what  consists  the  superiority  of  the  former  1 

(C.) 

200.  What  is  meant  by  Scientific  Explanation?  Give  illus- 
trations. 

(C.) 

201.  Explain  and  illustrate  how  Inference  is  involved  in  Obser- 
vation, and  how  Observation  is  involved  in  Experiment. 

(C.) 

202.  Distinguish  between  Term,  Proposition,  and  Syllogism. 
Show  how,  using  three,  and  only  three,  categorematic  words,  we 
may  form  with  them  either  (1)  a  single  Term,  or  (2)  a  Proposition, 
or  (3)  a  Syllogism. 

(C.) 

203.  What  is  the  difference  between  an  Index  Classification  and 
a  Natural  Classification  1 

(C.) 

204.  What  is  meant  by  Quality  and  Quantity  of  [Categorical] 

Propositions  ? 

If  an  I  proposition  is  given,  what  is  known  of  the  A,  E,  and  0 
propositions  in  which  the  same  pair  of  term  [name]s  appears  ? 

(C.) 


QUESTIONS  AND  EXERCISES. 


259 


205.  Point  out  some  of  the  most  important  characteristics  of  a 

(C.) 


good  observer. 


206.  How  would  you  define  Cause  ?    Would  it  be  correct  to 
assign  as  the  Cause  of  a  man's  writing  a  book  that  he  had  plenty 

of  time  ? 

(C.  shortened.) 

207.  How  would  you  (a)  explain, 

(6)  justify, 
any  belief — e.g.  that  every  great  general  has  a  Roman  nose,  that 
it  is  unlucky  to  walk  under  a  ladder,  that  water  freezes  at  32°  F., 
that  every  isosceles  triangle  has  the  angles  at  the  base  equal  ? 


208.  Why  does  the  thermometer  stand  so  low  in  the  hospital  in 
summer  ? 

{a)  Because  the  air  is  so  cool. 

{b)  Because  of  the  good  ventilation. 

(c)  Because  it  would  not  otherwise  be  healthy. 

(fZ)  Because  the  medical  authorities  have  ordered  it. 
In  what  sense  exactly  are  these   explanations  "t     Is  there  any 
common  element  in  them  all  ? 

(C.) 

209.  What  reasons  might  be  given  for  treating  of  the  Proposi- 
tion before  the  Term  in  a  system  of  Logic  ? 

(0.) 

210.  Show,  by  examples,  how  Induction  and  Deduction  are  both 
implicated  in  the  reasonings  of  common  life. 

(C.) 

211.  The  fall  of  bodies  and  the  planetary  motions  are  said  to  be 
'  suflaciently  explained'  by  being  referred  to  the  Law  of  Gravita- 
tion. Is  this  the  case  ?  How,  and  when,  are  we  entitled  to  say 
that  any  phenomenon  is  sufficiently  explained  ? 

(C.) 

212.  Show  that  Logic  requires  a  study  of  the  import  of  Terms 
and  Propositions. 

(0.) 

213.  Examine  the  following  :  — 

(1)  If  AisB,  CisD; 
IfEisF,  GisH; 
But  if  AisB,  E  is  F; 

.*.  If  C  is  D.  G  is  sometimes  H. 

(2)  The  crime  was  committed  by  the  criminal ; 
The  criminal  was  committed  by  the  magistrate  ; 
.*.  The  crime  was  committed  by  the  magistrate. 

(3)  A  dove  can  fly  a  mile  in  a  minute  ; 

A  swallow  can  fly  faster  than  a  dove  ; 

.'.  A  swallow  can  fly  more  than  a  mile  in  a  minute. 

(4)  The  ages  of  all  the  members  of  this  family  are  over  150  years ; 
The  baby  is  a  member  of  this  family  ; 

.*.  The  baby  is  over  150  years. 


Iggj 


gUgHg 


260 


QUESTIONS  AND  EXERCISES. 


(5)  Athletic  games  are  duties  ;   for  whatever  is  necessary  to 
health  is  a  duty,  and  exercise  is  necessary  to  health,  and  these 

games  are  exercise.  .      ,-     •  n 

(Adapted  from  Stock,  Deductive  Logic.) 

214.  In  Harriet  Martineau's  Autobiography  (vol.  i.  p.  355)  we 
are  told  that  a  certain  lady,  after  receiving  from  Charles  Babbage 
a  loner  explanation  of  his  celebrated  calculating  machine,  termi- 
nated" the  conversation  with  the  following  question:  'Now,  Mr 
Babbacre,  there  is  only  one  thing  more  that  I  want  to  know.  If 
you  put  the  question  in  wrong,  will  the  answer  come  out  right  r 

If  you  think  this  question  absurd,  give  distinct  and  detailed 
reasons  for  thinking  so,  and  reconcile  them  with  the  fact  that  false 

premisses  may  give  a  true  conclusion. 

(J.) 

215  It  has  been  said  that  much  of  what  seems  Observation  is 
really  Inference.  Explain  this,  and  illustrate  by  what  are  commonly 

called  '  deceptions  of  the  senses.' 

(0.) 

216.  In  what  sense  may  we  say  that  Genus  is  part  of  Species, 

and  in  what  sense  that  Species  is  part  of  Genus  ? 

(J.) 

217  I  am  asked  to  believe  that  A  will  be  elected  out  of  fifty 
similarly  equipped  candidates  ;  I  am  asked  to  believe,  when 
the  election  is  over,  that  A  has  been  elected.  Compare  these 
cases  with  reference  to  the  ground  and  measure  of  assent. 

(C.) 

218.  Distinguish  Observation  from  Experiment  and  from  Infer- 

(C.) 

219.  Write  a  short  essay  on  the  relation  between  Logic  and 

Mathematics. 

(C.  shortened.) 

220.  Examine  how  far  in  Economics  or  in  Politics  it  is  possible 

to  make  use  of  the  logical  Method  of  Difference. 

(C) 


QUESTIONS  AND  EXERCISES. 


261 


221.  Define  Experiment,  commenting  upon  the  following  state- 
ments : — 

(a)  We  cannot  set  experiment  over  against  observation  as  a  new 
method  of  knowledge. 

(6)  We  pass  upwards  by  insensible  gradations  from  pure  obser- 
vation to  determinate  experiment. 

(c)  Experiment  must  not  be  unqualifiedly  set  above  mere  obser- 
vation. 

(C.) 

222.  What  is  the  general  object  of  Mill's  Methods  of  Induction  ( 
State  the  Method  of  Concomitant  Variations,  with  an  illustration. 

(C.) 

223.  'A  good  temper  is  proof  of  a  good  conscience,  and  the 
combination  of  these  is  proof  of  a  good  digestion,  which,  again, 
always  produces  one  or  the  other.'  Show  (by  Euler's  diagrams  or 
otherwise)  that  this  is  precisely  equivalent  to  the  following :  '  A 
good  temper  is  proof  of  a  good  digestion,  and  a  good  digestion  of  a 
good  conscience.' 

(C.  modified.) 

224.  If  Mr.  X.  is  an  author,  authors  are  very  agreeable. 


INDEX  AND  VOCABULAEY. 


Absolute  —  Cf.  under  Terms, 
GategoHcal  Propositions,  and 
Ar<iuments. 

Abstract  Name.  According  to 
Mill  and  other  logicians,  an 
Abstract  Name  (or  Term)  is 
the  name  of  a  quality,  attribute, 
or  circumstance  of  a  thing. 
The  antithetical  term  is  Con- 
crete. 

Accidens — Cf.  Accident. 

Accident  (Predicable) — Note  ii. 

Inseparable — Note  ii. 

Separable — Note  ii. 

Added  Determinants,  Inference 
by — A  kind  of  Immediate  In- 
ierence  (EDUCTION)^  in  which 
some  fresh  determination  is 
added  to  the  terms  of  the  in- 
ferend,  94,  etc. 

Adjectives,  11. 

Affirmative  Conclusion  with  a 
Negative  Premiss,  191,  201. 

Agreement  and  Difference,  Joint 
Method  of  —  Cf.  Method  of 
Agreement  in  Presence  and 
Absence. 

Agreement  in  Presence  and  Ab- 
sence, Method  of — Cf.  Method 
of  Agreement  in  Presence  and 
Absence. 

Agreement,  Method  of  —  Cf. 
Method  of  Agreement, 

All,  69,  71. 

ALTERNATIVE  (or  Disjunc- 
tive) MEDIATE  INFER- 
ENCES, 153-156. 

Defined,  153. 

Divided,  153-154,  156. 

Canons  of,  154-155. 


A  L  TERN  A  TI VE  PRO  POSI- 
TIONS, 52-57. 

,  CONTINGENT,  54,  57. 

,  FORMAL  (or  SELF-CON- 
TAINED), 53,  54,  57. 

,  SELF-CONTAINED— Qi. 


Formal. 

SUBSUMPTIONAL,  53, 


54,  57. 

Ambiguous  Middle  Term  —  A 
Middle  Term  which  has  (or 
may  have)  a  different  applica- 
tion in  one  Premiss  from  what 
it  has  in  the  other;  119,  188, 
etc.,  201. 

Ambiguous  Term,  172. 

Ampliative  Proposition — A  Cate- 
gorical Proposition  in  which 
the  signification  of  the  Predicate 
is  not  included  in  that  of  the 
Subject — opposed  to  Essential 
or  Verbal,  or  Explicative,  or  Ana- 
lytic Proposition.  Ampliative 
Propositions  are  called  also  Real 
or  Synthetic. 

Analogy,  146. 

Analysis — the  operation  of  break- 
ing up  a  whole  into  parts — 
opposed  to  Synthesis.  The 
process  of  discovering  laws  by 
examination  of  facts  isf  requently 
described  as  analytic.  Hence 
it  is  said  that  the  Method  of 
Analysis  is  the  Method  of  Dis- 
covery. 

Analytic  Proposition  —  Cf.  Es- 
sential  Proj>osition. 

Antecedent— (1)  An  event  which 
precedes  another  is  an  ante- 
cedent to  that  other  ;  (2)  The 


1  New  Technical  Terms  are  printed  in  italic  capitals. 


263 


^aaiiiifiiii^       "-^^'^^immsmm^mim 


264 


INDEX   AND   VOCABULARY. 


first  clause  of  a  Hypothetical 
or  Conditional  Proposition  is 
called  its  Antecedent,  42,  etc. 

Ani/,  69-71. 

Application  of  Names  and  Terms, 
5,  6,  20. 
posteriori  knowledge — Know- 
ledge obtained  from  experience 
either  (1)  originally — as,  e.g., 
the  knowledge  we  have  that 
vaccination  is  a  preservative 
against  small-pox,  or  (2)  by 
fresh  appeal  to  experience,  as  I 
may  know  by  now  rubbing  two 
pieces  of  wood  together  that 
heat  is  a  consequent  of  fric- 
tion. 

A  priori  knowledge — Knowledge 
not  obtained  by  experience — 
either  (1)  not  at  all,  as,  the 
knowledge  that  A  is  B  or  not  B; 
or  (2)  not  by  fresh  appeal  to 
experience,  as,  the  knowledge 
we  now  have  that  vaccination 
is  a  preservative  against  small- 
pox. 

Arbor  P or phyriana  —  Cf.  Tree  of 
Porphyry. 

Argument  —  Cf.  Mediate  Infer- 
ences. 

An  Argument  (or  Mediate 

Inference)  consists  of  three  Pro- 
positions, of  which  two  are 
called  the  Premisses,  and  the 
third  the  Conclusion.  The 
Conclusion  is  inferred  from  the 
Premisses  taken  together. 

Argument — d  fortiori,  14,  34,  37, 
130-131. 

Argument — Relative  Categorical, 
80,  129-132. 

Canon  of,  132. 

Arguments,  Absolute  (cf.  Syl- 
loyism) — An  Absolute  Argument 
(or  Syllogism)  is  an  Argument 
that  is  formal,  or  of  absolutely 
general  validity,  by  virtue  of 
its  mere  form.  Thus  M  is  P 
and  S  is  M, ,  *.  S  is  P,  is  an  Ab- 


solute Argument,  because  the 
reasoning  holds,  no  matter 
what  words  or  symbols  we  put 
in  the  place  of  M,  P,  and  S. 
Cf  pp.  80,  114,  etc. 

Arguments,  Relative — A  Relative 
Argument  is  an  Argument  that 
is  not  in  a  form  which  is  of  ab- 
solutely general  validity.  This 
characteristic  follows,  of  course, 
from  the  fact  that  the  cogency 
of  any  Relative  Inference  de- 
pends upon  the  constitution  of 
the  system  to  which  it  refers. 
Cf  pp.  80,  114. 

Anjumentnm  ad  hominem — An 
argument  that  has  a  special 
application  to  a  given  indi- 
vidual. The  name  is  sometimes 
applied  to  a  valid  argument, 
which  starts  from  premisses 
admitted  by  the  person  to  whom 
it  is  addressed — cf.  Arffumen- 
tum  ex  conresso  ;  sometimes  to 
a  more  or  less  fallacious  argu- 
ment, of  the  kind  called  Irrele- 
vant Conclusion.  To  attack 
an  opponent's  character  instead 
of  answering  his  reasons,  is  a 
fallacy  of  this  kind. 

Argumentum  ad  judicium  —  An 
appeal  to  judgment  or  common 
sense. 

Argumentum  ad  verecundiam — An 
appeal  to  modesty  or  reverence. 

Argumentum  ex  concesso — An  ar- 
gument which  starts  from  what 
has  been  admitted  or  conceded. 

Aristotelian  Induction — Cf.  Per- 
fect Induction. 

Aristotle's  Dictum — Cf.  Dictum 
de  omni  et  nulla. 

Assertion  —  An  Affirmation  or 
Denial. 

Assumption — A  Proposition  which 
is  taken  for  granted,  without 
being  either  self-evident  or 
proven. 

Axiom — A  Self-evident  Principle, 


INDEX    AND    VOCABULARY. 


265 


a  Proposition  which  is  both 
fundamental  and  self-evident. 
'  There  seem  to  be  four  con- 
ditions, the  complete  fulfilment 
of  which  would  establish  an 
apparently  self-evident  pro- 
position in  the  highest  degree  of 
certainty  attainable  ' ;  it  must 
*  {a)  have  the  terms  clear  and 
precise ;  (6)  be  really  self- 
evident  ;  (a)  not  conflict  with 
any  other  accepted  proposition  ; 
(c?)  be  supported  by  a  concensus 
of  experts.'  Cf  Sidgwick, 
Methods  of  Ethics,  Bk  iii.  Ch.  xi. 

Basis  of  Division — the  point  or 
points  upon  which  a  division  is 
based.  E.g.  in  the  division  on 
p.  161  the  Basis  of  Division  of 
(1)  into  (2),  (3),  and  (4)  is  com- 
parative length  of  sides. 

Bramantip,  Celarent,  etc.,  123. 

Catecjorematic  (p.  85)— A  word 
is  Categorematic  if  it  can  be 
used  as  the  Subject  or  Predicate 
of  a  Categorical  Proposition. 

Category  (or  Predicament) — *  A 
term  (meaning  literally  **  Pre- 
dication" or  "Assertion")  given 
to  certain  general  classes  of 
terms,  things,  or  notions  ;  the 
use  being  very  different  with 
different  authors '  (Murray's 
New  English  Dictionary).  Aris- 
totle enumerates  ten  Cate- 
gories :  Substance,  Quantity, 
Quality,  Relation,  Action,  Pas- 
sion, Where,  When,  Posture, 
Habit.  Mill  understands  by  the 
Categories  the  Sumnia  Genera 
of  nameable  things  ;  his  Cate- 
gories are  :  Feelings,  Minds, 
Bodies,  Certain  Relations  of 
Feelings  (Co-existences,  Se- 
quences, Similarities,  and  Dis- 
similarities).    Kant's  four  chief 


Categories  are  Quantity,  Quality, 
Relation,  and  Modality,  corre- 
sponding to  the  different  forms 
of  judgment. — The  Categories 
indispensable  to  Assertions,  In- 
ferences, Classing,  and  Syste- 
matising  are — (1)  Identity  in 
Diversity ;  (2)  Similarity  in 
Otherness  ;  (3)  Unity  of  Parts 
and  Whole  ;  these  may  there- 
fore be  called  the  principal 
Logical  Categories. 

Categories,  74,  75,  211. 

Categorical  Propositions,  20,  41. 

Import  of,  20  seq. ,  62-64. 

Classification  of,  30-32,  33. 

COINCIDENTAL,  30. 

ADJECTIVAL,  30. 

Whole,  30. 

Partial  (or  Particular),  30. 

A  T  TBI  BUTE,  30. 

SUBSTANTIVAL,  33. 

P  BO  PER  and  UNIQUE,  30. 

SPECIAL,  30,  33. 

COMMON,  30. 

Universal,  30. 

General,  .30,  32. 

Definite,  30,  31. 

Indefinite,  30,  31. 

Absolute,  14,  30,  31,  36. 

Distributive,  30,  31. 

Collective,  30,  31. 

Affirmative,  31,  33. 

Negative,  31,  33. 

Mathematical,  14,  37-41. 

Relative,  14,  30,  31,  34-41. 

Analysis  of,  36. 

Categorical  Mediate  Inferences 
(Categorical   Arguments),    114- 


132. 


Definition  of,  114. 
Divisions  of,  87,  114. 


Categorical  Syllogisms,  Canon  of, 

116. 
Application  of    Canon    of, 

116-117. 

Rules  of,  118. 

Breaches  of  Rules  of,  118, 

119.     Cf.  Fallacies. 


I 


mmmmmmmmimm 


266 


INDEX   AND   VOCABULARY 


CATEGORICO  -  ALTERNA- 
TIVE ARGUMENTS,  153, 
etc.,  156. 

Cause  and  Effect — If  any  con- 
junction CX  is  related  to  any 
change  E  in  such  a  way  tliat 
CX  cannot  occur  without  E,  nor 
E  without  CX :  then  CX  is  cause 
of  E,  and  E  is  effect  of  CX— 
135. 

Chain-Argument — Cf.  Sorites. 

Character,  5,  6,  20. 

Circular  Definition  {Circidus  in 
Definiendo,  Vicious  Circle) — A 
Circular  Definition  (including 
Tautological  Dejinition)  is  a 
definition  which  merely  repeats 
the  word  to  be  defined,  or  brings 
us  back  to  it,  66,  67,  168,  184. 

Circuhis  in  Probanda  (Circular 
Fallacy^  Begging  the  Question), 
197-199. 

Circumstantial  Evidence  —  '  In- 
direct Evidence  inferred  from 
circumstances  which  afford  a 
certain  presumption,  or  appear 
explainable  only  on  one  hypo- 
thesis'  (Murray's  New  English 
Dictionary). 

Classification,  158,  \o9  seq.,  162. 

Rules  of,  161. 

Artificial — An  Arrangement 

of  Classes  which  is  for  some 
special  purpose  and  is  not  ob- 
viously suggested  by  the  things 
classified.  It  is  opposed  to 
Natural  Classification,  which  is 
useful  for  general  purposes,  and 
is  suggested  by  the  things 
themselves.  The  terms  Arti- 
ficial and  Natural  as  applied  to 
Classification  might  with  ad- 
vantage be  replaced  by  the 
terms  General  and  Special,  for 
all  Classification  (cf.  p.  164)  is 
to  some  extent  artificial,  as 
being  made  by  man  for  his 
purposes,  and  also  to  some  ex- 
tent natural,  because  it  must 


be  in  accordance  with  the 
nature  of  the  things  classified. 

Classification  by  Type — In  this 
phrase  Classification  is  used  in 
the  sense  of  Classing.  It  was 
held  by  Whewell  that  natural 
groups  are  given  not  by  Defini- 
tion but  by  Type,  i.e.  by  refer- 
ence to  '  an  example  which 
possesses  in  a  marked  degree 
all  the  leading  characters  of  the 
class.'  In  classing  by  type  the 
appeal  is  rather  to  general  re- 
semblance than  to  the  possession 
of  a  fixed  list  of  characteristics. 

Classification  by  Series  —  This 
phrase  is  used  to  indicate  an 
arrangement  of  things  in  which 
the  classes  are  so  grouped  with 
reference  to  some  characteristic 
or  group  of  characteristics,  that 
they  present  a  kind  of  hierarchy 
of  classes.  E.g.  in  Zoology,  any 
class  is  higher  in  the  classifica- 
tion in  proportion  as  it  is  held 
to  have  more  or  fuller  life. 

Classification,  Index — Cf.  Index 
Classification. 

Classing,  75,  158,  161-162. 

and  Definition,  158,  168-169. 

(as  well    as    Classification) 

may  be  Natural  or  Artificial, 
General  or  Special. 

Collective  Term — A  Term  which, 
in  the  singular  number,  applies 
to  a  plurality  of  objects  of  the 
same  kind,  e.g.  library,  army, 
school.  (The  antithetic  term 
is  Non-collective.) 

'Collective  use'  of  Terms. — A 
Term  used  collectively  applies 
to  the  whole  only,  and  not  to 
the  separate  constituents,  of  a 
group  or  class.  The  antithetic 
term  is  *  Distributive  use. ' 
The  distinction  between  '  Col- 
lective use  '  and  *  Distributive 
use  '  is  appropriate  only  in  refer- 
ence to  plural  Terms,  30,  31. 


INDEX   AND   VOCABULARY. 


267 


Colligation   of    Facts — A    phrase 
used  by  Whewell  to  signify  the 
connecting  or  systematising  of 
facts   by   some   suitable    hypo- 
thesis or  notion. 
Combination  of  Causes — An  inter- 
mixture of  causes  producing  a 
Heteropathic  Effect. 
'  Combined  '  ('Complete')  Method 
(  =  Mill's    Hypothetical    M.  )— 
Note  V. 
Complementary   Premisses — Two 
Propositions,  from  which,  taken 
together,  a  Conchision  may  be 
drawn,  72.     Cf.  Premis.sal  Pro- 
positions. 
*  Complete  Induction  ' — Cf.  *  Per- 
fect Induction.^ 
Complex  Conception,  Inference  by 
— This  is  a  kind  of  Immediate 
Inference,  in  which  Terms  that 
have  the  same   application  are 
made  more  complex,  93,  94,  95. 
(Complex  or  Intermixed  Effect — 
An   effect   which    results  from 
the  conjunct  action  of   two  or 
more  causes. 
Composition  of  Causes — An  inter- 
mixture of  Causes  producing  a 
Compound  Effect. 
Compound     Effect — A     Complex 
Effect  which  is  equivalent  to  the 
sum    of    the    separate    effects. 
(Cf.  Parallelogram  of  Forces.) 
Comprehension — Cf.  Connotation. 
Conceptualist    view    of    General 
Names.     On    this   view,    there 
corresponds   to   every    General 
Name  a  General  Notion  in  the 
mind,    which    is    the    '  mental 
equivalent '  of   the   name,    and 
applies  equally  to  all  the  par- 
ticular  objects    called    by   the 
name.   Cf.  Section  xvii.  ,175,  etc. 
Conclusion,  86,  115. 
Concomitance,  135. 
Concomitant  Variations,  Method 
of — Cf.  Method  of  Concomitant 
Variations. 


Concrete     Name— According     to 
Mill  and  later  logicians,  a  Con- 
crete Name  is  the  name  of  a 
thing.     Cf.  Abstract  Name. 
CONDITIO  -  ALTERNATIVE 

— Cf .  Inferentio- Alternative. 
CONDITIO  -  CATEGORICAL 

Argument,  150,  152. 
Confusion  and  Fallacy,  178  seq. 
Conjunctions,  force  and  justifica- 
tion of,  75-77. 
Connotation — By  Connotation    of 
a   Name    'we  mean   the   attri- 
butes on  account  of  which  any 
individual   is    .    .    .    called  by 
the  name'  (Dr.  Keynes).     Dr. 
Keynes  suggests  differentiating 
the  terms  ( 1 )  Connotation,  (2)  In- 
tension, (3)  Comprehension,  as 
follows:  — (1)  =  the     attributes 
implied  or  signified  by  a  name  ; 
(2)  =  the  attributes  mentally  as- 
sociated with  the  name,  whether 
or  not  they  are  actually  implied 
by  it ;    (3)  =  all  the  attributes 
possessed  in  common  by  all  the 
objects  denoted  by  the  name. 
Connote — Cf.  Connotation. 
Consequent—  ( 1 )  Of  two  successive 
events,  the  later  is  consequent 
to  the  earlier  ;  (2)  The  second 
Clause    of    a   Hypothetical    or 
Conditional  Proposition  is  called 
its  Consequent,  42. 
Consilience    of    Inductions — This 
is  a  phrase  of  Whewell's,  ap- 
plied to   the   case  in  which   a 
plurality  of  Inductions  support 
the  same  Hypothesis. 
Constituent  Class — Any  one  of  a 
plurality    of   sub-classes  which 
constitute  a  wider  class.     The 
wider    class    so    divided    is    a 
Genus  of  which  the  sub-classes 
are  Species,  160,  161. 
Constituent    Species  —  Cf.    Con- 
stituent Class. 
Constructive  Syllogism — Cf.  Mo- 
dels Ponens. 


LrAfc..'j3tiM|gj^ 


268 


INDEX   AND   VOCABULARY. 


Continuity,  Law  of— This  ex- 
presses the  principle  that  every 
change  is  a  continuous  process, 
that  there  can  be  no  gap  or 
skipping  in  passing,  e.g.irom  one 
degree  of  temperature,  or  one 
time,  or  place,  or  size,  to  another. 
The  same  principle  is  expressed 
in  the  saying,  Natura  noii  facit 
saHum  (or  Natura  non  arjit  i^tr 
saltnm). 

Contradiction,  Law  of,  206,  20S- 

209. 

is  the  Principle  of  Con- 
sistency, 209. 

Contradictories— Note  i. 

Contradictory— Two  propositions 
are  contradictory  (a)  when  one 
is  the  negative  of  the  other;  {?>) 
when  they  are  A  and  O,  or  E 
and  I  (which  are  mutually  ex- 
clusive and  together  exhaustive), 

108,  109. 

Contraposition,  Contraposit — Cf. 
Cont7'aversion,  Contr avert. 

Contrary,  Contraries,  108,  109, 
Note  I. 

CONTRA  VERSE— The  proposi- 
tion reached  by  Contraversion. 

CONTRA  VERSION  (Contra- 
position), 88,  96-97  ;  94,  note  ; 
101-102,  104-105,  107. 

CONTRA  VER  T  (Contraposit),  to 
perform  the  process  of  Contra- 
version. 

CONTRA  VERT  END— The  Pro- 
position to  be  coutraverted. 

Converse  —  The  proposition 
reached  l^y  Conversion. 

Conversion,  32,  88,  89-90,  99-100, 
103,  107. 

Conversion  per  Accidens — Conver- 
sion of  A  to  I. 

Conversion  by  Negation— Same  as 
Contraposition. 

Conversion  and  Quantification, 
58-66. 

Convert— To  perform  the  process 
of  Conversion. 


Convertend— The  proposition  to 
be  converted. 

Co-ordinate  Classes  —  Consti- 
tuent Classes  belonging  to  the 
mmt  stage  of  a  division,  161. 

Copula,  5,  8,  9,  16-17. 

Correlative  Terms— Terms  which 
have  a  certain  special  relation 
to  each  other,  the  thing  re- 
ferred to  by  one  member  of  a 
pair  of  correlatives  implying 
also  the  thing  referred  to  by 
the  other  member — as,  f.f/.,  in 
Sovereign  and  Subject,  Whole 
and  Part. 

Criterion— A  standard  or  test  by 
which  to  judge. 

Cross  Division— A  division  in 
which  Constituent  Classes  over- 
lap, 161,  184. 

Data— Statements  given  or  ac- 
cepted. 

Deduction,  81-85,  87,  120,  etc., 
133-134. 

Meaning  of,  81. 

'  Deductive  Method '  of  Induction 

— Note  V. 

Abstract— When    the 

Deductive  Method  is  applied  in 
sciences  that  are  not  concerned 
with  Causation  {e.g.  Mathe- 
matics), it  is  called  by  Mill  the 
Abstract  Deductive  Method. 

Concrete— Mill    gives 

this  name  to  the  Deductive 
Method  when  it  is  applied  in 
sciences  that  are  concerned  with 
phenomena  of  Causation — e.g. 
Sociology,  Medical  Science. 

Direct — Cf.    Inverse 

D.  M.  In  this  application  of 
the  Deductive  Method,  we  first 
reach  a  conclusion  by  deduc- 
tion from  the  results  of  previous 
Inductions,  and  then  verify  by 
comparison     with     experience. 

Note  V. 
Inverse— In  this  appli- 


INDEX   AND   VOCABULARY 


269 


cation  of  the  Deductive  Method 
'  we  obtain  our  law  more  or  less 
conjecturally  by  direct  experi- 
ence, and  afterwards  verify  it 
by  showing  that  it  is  deducible 
from  more  general  or  better 
known  laws.' 

De  facto — Wliat  is  actually  or 
infact. 

De  jure — What  ought  to  be, 
what  is  legally  or  by  right. 

Definition,  158,  160,  163  seq. 

and  Language,  163-177. 

,  Rules  of,  168. 

Defined,  163. 

and  Recognition,  164-166. 

•  (Predicable)— Note  ii. 

Accidental— Cf.  Description. 

Genetic—'  An  indication  of 

the  way  in  which  the  mental 
picture  '  of  the  thing  to  be  de- 
fined *  may  or  must  be  formed. 
"  Let  a  straight  line  revolve  in 
one  plane  about  one  of  its  ex- 
tremities, and  combine  the  suc- 
cessive positions  of  the  other 
extremity  " — that  is  a  Genetic 
Definition  of  a  circle  '  (Lotze). 

Demonstration— Absolute  Proof 
(or  Unquestionable  Evidence). 

Denial  (Contrary  and  Contradic- 
tory), 109. 

Denotation — By  Denotation  of  a 
name  is  meant  the  individuals 
to  which  the  name  applies. 

Denote — Cf.  Denotation. 

Depth — Cf.  Connotation. 

Description — An  account  of  any- 
thing which  is  not  precise 
enough  to  be  called  a  Defini- 
tion, but  which  is  sufficient  to 
mark  off  the  thing  described 
from  other  things. 

Destructive  Syllogism— Cf.  Modiis 
Tollens. 

Desynonymization  —  The  term 
used  by  Coleridge  for  Differen- 
tiation^ which  see. 

Determination— Distinguishing  or 


limiting  by  addition  of  charac- 
teristics. E.g.  when  I  qualify 
the  term,  flov-er  by  the  adjective 
recZ,  jloicer  has  undergone  De- 
termination. 

Dictum  de  omni  et  nulla,  93,  123, 
123  note. 

Difference  —  means  (1)  Distinct- 
ness or  Otherness;  (2)  Diversity. 

Method   of— Cf.   Ilethod  of 

Difference. 

Differentia  (Difference)  —  The 
characteristics  by  which  any 
sub-class  (or  species)  is  distin- 
guished [differenced]  from  the 
rest  of  its  wider  containing 
class  (or  Genus),  160,  Note  ii. 

Differentiation  of  Terms  —  The 
specialising  process  by  which 
words  originally  synonymous 
come  to  have  a  different  use 
and  application — e.g.  big,  large^ 
great. 

Dilemma — A  Dilemma  is  an  In- 
ferentio- Alternative  Argument, 
having  a  Compound  Inferential 
Major,  an  Alternative  Minor, 
and  a  Conclusion  which  is  either 
Alternative  or  Categorical.  In 
a  strict  Di-lemma  the  Minor 
Premiss  contains  only  two  Al- 
ternatives. Cf.  Infey^entio- Alter- 
native Argument,  154. 

Complex  —  In    a    Complex 

Dilemma  the  Conclusion  is 
Alternative. 

Simple — In  a  SimpleDilemma 


the  Conclusion  is  Categorical. 
—     Constructive — In    a     Con- 
structive Dilemma  the  Conclu- 
sion is  Affirmative. 

Destructive— In  a  Destruc- 


tive Dilemma  the  Conclusion  is 

Negative. 
Disjunctive.     See  Alternative. 
Dissimilarity,   Principles  of,  147, 

207. 
Distinctness(  =  Otherness)— There 
is  Distinctness  between  any  two 


270 


INDEX    AND   VOCABULARY. 


objects — if  A  is  not  B,  then  A 
is  distinct  from  B. 

Distributed  Term — A  term  is  said 
to  be  distributed  if  it  is  taken 
universally,  i.e.  if  the  whole  of 
the  class  or  group  to  which  it 
refers  is  explicitly  taken.  E.;/. 
A  in  All  A  is  distributed,  in 
Some  A,  undistributed.  In 
Affirmative  Categorical  Pro- 
positions the  Predicate-name  is 
undistributed ;  in  negatives,  the 
Predicate-name  is  distributed. 

*  Distributive  use  '  of  Terms  —  A 
term  is  used  distributively  when 
it  applies  to  the  separate  con- 
stituents of  the  group  or  class 
to  which  it  refers — (Cf.  Col- 
lective  use),  30,  31. 

Diversity,  Diverse  —  There  is 
Diversity  between  two  things 
when  they  are  unlike  each 
other ;  and  between  two  states 
of  the  same  thing,  if  the  thing 
has  altered.  Cf. 20-25 />asvjm, 29. 

Division,  158  seq. 

Rules  of,  161. 

and  Classification,  158,  159- 

161. 

by    Dichotomy.     Note   ii., 

p.  217. 

EDUCE,  EDUCEXl),  EDUCT, 
EDUCTION,  defined,  86  (cf. 
108). 

EDUCTIONS  (Immediate  Infer- 
ences), 88-107. 

EflFect— Cf.  Cause  and  Effect. 

Elimination — Removing  or  drop- 
ping out  Elements  or  Consti- 
tuents. Elimination  is  usual  in 
processes  of  Mediate  Inference — 
e.g.  in  the  Syllogism  M  is  P 
and  S  is  M .'.  S  is  P,  the  term  M 
is  dropped  out  in  the  conclusion. 
By  Elimination  of  Chance  is 
meant  calculating  and  leaving 
out  of  account,  in  any  inquiry, 
the  influence  of  casual  factors. 


Elliptical  Arguments — Note  iv. 

Empirical  Law — A  Law  crudely 
generalised  from  experience, 
and  asserting  an  interdepend- 
ence [cf  Section  xiii.)  which  is 
neither  self-evident,  nor  proved 
by  the  Inductive  Methods — a 
sort  of  quack  Law.  Cf.  Induc- 
tion by  simple  enumeration. 

Method — The  method  of  un- 
reasoned appeal  to  experience. 
A  method  in  which  there  is 
crude  and  unjustified  generalisa- 
tion from  facts. 

P^nthymemes — Note  iv. 

of  the  First  Order  ; 

of  the  Second  Order ; 

of    the   Third   Order  —  Cf 

Note  IV. 

Enumeratio  Simplex — Cf.  Indtic- 
tion  by  Simple  Enumeration. 

Epicheirema — Note  iv. 

Epi-syllogism  — Note  iv. 

Equal,  .38,  41. 

Equipollent— Cf.  Equivalent. 

Equivalent — Definition  of,  85,  86. 

Equivalent  Propositions — Propo- 
sitions which  are  reciprocally 
inferrible,  72. 

Equivocal  Terms— Cf.  Ambiguous 
Terms. 

Essential  Proposition — A  Cate- 
gorical Proposition  in  which  the 
Predicate  repeats  all  or  part  of 
the  signification  of  the  subject. 
Essential  Propositions  are  called 
also  Analytic  and  Verbal.  The 
term  Feria/ seems  specially  ap- 
plicable to  propositions  in  which 
the  Predicate  is  a  Definition  or 
a  Synonym  of  the  Subject. 

Euler's  Diagrams — Circular  Dia- 
grams such  as  are  used  at  p.  25, 
etc.,  are  so  called,  because  used 
by  Euler,  a  Swiss  logician  of 
the  last  century. 

Event— Change  in  Subjects  of 
Attributes,  136. 

EVERSIONS,    80,     88  ;      Cate- 


INDEX    AND   VOCABULARY. 


271 


gorical,  89-99,  107;  INFER- 
ENTIAL, 99-103,  107;  AL- 
TERNATIVE, 103-105,  107. 

Example,  Argument  from— This 
consists  in  arguing  from  a  sample 
to  the  whole,  and  except  in  the 
case  of  mathematical  examples, 
is  not  a  cogent  mode  of  infer- 
ence. 

Exceptive  Proposition — A  Cate- 
gorical Proposition  of  the  form 
All  A,  except  B,  is  C. 

Excluded  Middle,  Law  of,  204, 
209. 

a  Principle  of  Comple- 
tion, 209. 

Exclusive  Proposition — A  Cate- 
gorical Proposition  of  the  form 
A  alone  are  B,  Only  C  are  Z>, 
None  but  X  are  Y,  etc. 

Exhaustive  Division — A  Division 
which  includes  every  possible 
case.  Division  by  Dichotomy  is 
sometimes  called  Exhaustive 
Division. 

Existence,  5,  6,  20. 

Experiment^An  Experiment  is 
made  when  certain  conditions 
of  an  event  are  purposely  ar- 
ranged in  a  certain  way,  and 
then  the  event  so  conditioned 
is  observed. 

Experiment um  Crucis — A  Crucial 
or  Decisive  Experiment. 

^Explanation  —  In  the  broadest 
sense  Explanation  of  any  fact 
or  statement  may  be  described 
as  showing  its  connection  with 
some  other  facts  or  statements. 
Explanation  is  often  used  in 
the  narrower  sense  of  showing 
the  cause  of  anything.  Explana- 
tion is  to  be  carefully  distin- 
guished from  Justification. 

Explicative  Proposition  —  Cf. 
Essential  Proposition. 

EXTRA  VERSION  — A  kind  of 
Eduction  in  which  from  the 
modification  of  one  of  two  terms 


which  have  identical  applica- 
tion, we  infer  a  precisely  similar 
modification  of  the  other  term, 
88,  94-96,  96  note,  101,  104,  107. 
Extremes  of  a  Categorical  Pro- 
position— Its  ends  or  termini — 
i.e.  the  Subject  and  Predicate. 

Fallacy,  118-119,  178-201. 

Definition  of,  183,  184. 

Division  of,  178-199  passim, 

200,  201. 

ABSOLUTE,  178-199  pas- 


sim, 200,  201. 

of  Accent — A  case  of  mis- 


take which  arises  from  accen- 
tuating the  wrong  word  in  a 
sentence. 

—  of  Accident  {A  dido  simpli- 
citer  ad  dictum  secundum  quid), 
179,  181. 

-,  Converse  {A  dicto  secun- 


dum quid  ad  dictum  simpliciter), 
179,  181. 

—  ALTERNATIVE  (or  Dis- 
junctive), 186-187, 195-197,  etc.. 
200,  201. 

of  Ambiguous  Middle,   118, 


119,  188,  201. 
—  of  Amphibology  (or  Amphi- 
boly), 179. 

of    the    Antecedent  —  This 


consists  in  denying  the  Ante- 
cedent in  an  Inferentio-Cate- 
gorical  Argument,  194. 

—  of  Arguing  from  one  special 
case  to  another  special  case  {A 
dicto  secundum  quid  ad  dictum 
secundum  alterum  quid),  180. 

—  of  Argumentum  ad  populum 
— This  is  a  species  of  the  Fallacy 
of  Irrelevant  Conclusion,  and 
consists  in  an  appeal  to  the 
sentiments  rather  than  to  the 
reason  of  any  collection  of  per- 
sons to  whom  it  is  addressed, 
183. 

—  Categorical,  185,  187-193, 
198,  etc.,  200,  201. 


272 


INDEX   AND   VOCABULARY. 


Fallacy  of  Composition,  179,  180. 

of    the    Consequent  —  This 

consists  in  affimiiiKj  the  Conse- 
quent of  an  Inferentio-Cate- 
gorical  Argument,  195. 

of   Continuous   Questioning 

(or  of  Many  Questions),  178- 
179. 

of  Definition,  184. 

of    DISCUXTINUITY  — 

In  Fallacies  of  Discontinuity 
there  is  a  breach  of  the  osten- 
sible connection  upon  which  the 
meaning  or  validity  depends, 
183,  184,  185,  etc.,  '200,  201. 

of  TAUTOLOGY— In  Fal- 
lacious Tautology  there  is  mere 
repetition  under  the  guise  of 
difference.  Tautological  Fal- 
lacies of  Categorical  Syllogism 
are  excluded  by  the  definition 
of  Syllogism  —  183,  184,  185, 
etc.,  200,  201. 

of  Division,  179-180. 

of   Division   and  Classifica- 


tion, 184. 

—    of    EDUCTION    (or 
mediate    Inference),    180, 
182,    etc.,    184,    185-187, 
201. 


Im- 
181, 
200, 


200. 


ELEMENTAL,   183,   184, 


—  of  Equivocation,  179-180. 

—  EVE  RSI  Fi;— These  are  Fal- 
lacies of  Immediate  Inference 
(or  Eduction)  which  occur  in 
passing  from  a  given  proposi- 
tion to  another  proposition  of 
the  same  form,  e.g.  from  a  Cate- 
gorical to  a  Categorical,  185, 
etc. 

of  False  Cause  {A  non  Causa 


pro  Causa,  Post  hoc  ergo  propter 
hoc).  In  this  Fallacy,  Causa- 
tion is  inferred  from  mere  Ante- 
cedence, 181-182. 
of  Figure  of  Speech— A  Fal- 
lacy which  arises  from  mistak- 
ing one  part  of  speech  for  an- 


other, or  a  word  of  Jirst  inten- 
tion for  a  word  of  second  inten- 
tion, etc. 

Fallacy,  Formal— Cf.  Absolute  Fal- 
lacies^. 

of  FOUR  TERM-NAMES, 

187,  etc.,  201. 

of   Illicit  Major — Here  the 

Major  Term  is  distributed  in 
the  Conclusion  but  not  in  the 
Premisses,  119,  191,  201. 

of  Illicit  Minor — Here  the 

Minor  Term  is  distributed  in 
tlie  Conclusion  but  not  in  the 
Premisses,  119,  190-191,  201. 

of     INCONSISTENT 


PREMISSES,  187,  190,  201. 

—  INFERENTIAL,  185-186, 
193-195,  198-199,  200,  201. 

—  of  Irrelevant  Conclusion 
{Ignoratio  Elenchi)  —  In  this 
Fallacy  the  Conclusion  is  proved , 
but  it  is  a  Conclusion  more  or 
less  different  from  the  one  whicli 
ought  to  have  been  proved,  182, 
183. 

—  of  Judgment — Cf.  Elemental 


Fallacies. 

—  '  Logical ' — Fallacies  which 
break  the  laws  of  Assertion  or 
Inference.  Cf.  Section  xviii. 
passim,  and  Tables  xi.  and  xii. 

—  '  Material ' — Fallacy  of  Acci- 
dent, Converse  Fallacy  of  Ac- 
cident, Irrelevant  Conclusion, 
Petitio  Principii,  Non  Sequitur, 
False  Cause,  Fallacy  of  Many 
Questions,  etc.,  have  been  called 
Material  Fallacies,  as  opposed 
to  the  so-called  Logical  and 
Semi- Logical  Fallacies.  Section 
xviii.,  178-184. 

—  of   NO   TRUE   MIDDLE 


TERM,  118, 119,  181,  etc.,  187- 
189,  201. 

—  of  Negative  Conclusion  from 
Affirmative  Premisses,  191, 
201. 

—  of    Non-Sequitur  —  In  this 


INDEX   AND  VOCABULARY. 


273 


Fallacy,  the  Conclusion  does  not 
follow  from  the  Premisses,  181, 
187,  190. 

Fallacy  of  Petitio  Principii — This 
is  a  Circular  Fallacy,  a  Fallacy 
which  occurs  when,  in  the  at- 
tempt to  prove  an  assertion, 
recourse  is  had  to  some  proposi- 
tion which  that  assertion  itself 
has  contributed  to  prove,  197- 
199. 

oi  REDUNDANT  TERMS 

— Cf.  Fallacies  of  Discontinuity, 
180,  181,  201. 

RELATIVE,  199,  200. 

The  Falla- 


*  Semi-Logical 


cies  which  have  been  so  called 
are  those  of  Equivocation,  Am- 
phibology, Composition,  Divi- 
sion, Accent,  Figure  of  Speech. 
Syllogistic  (included  in  Fal- 


lacies of  Mediate  Inference),  184- 
185,  187-199,200,  201. 

TRA  NS  VERSI F^— These 


Fallacies  of  Immediate  Inference 
(or  Eduction)  occur  in  passing 
from  a  given  proposition  to  a 
proposition  of  a  diflferent  form, 
e.g.  from  a  Categorical  to  an 
Inferential,  185,  etc. 

of  Undistributed  Middle- 
Here  there  is  no  true  Middle 
Term, because  the  Middle  Term- 
name  has  some  for  Term-Indi- 
cator in  both  Premisses,  188  (6), 
etc.,  201. 

Fallacious  Questioning — Cf.  Fal- 
lacy of  Continuous  Question- 
ing. 

Few,  meaning  of,  69. 

Figure,  122  seq.,  160. 

Definition  of,  etc.,  122  seq. 

Form — This  expression  as  used  by 
Francis  Bacon  signifies  an  in- 
variable co-existent  which  he 
supposed  to  accompany  every 
property  of  an  object,  205-206. 
Cf  137. 

Formal,  Meaning  of,  80. 


'  Formal  Induction  '— Cf.  'Perfect 
Induction. ' 

Fujidamenttnn  divisionis  —  Cf. 
Basis  of  Division. 

Fundamental  Syllogism — A  Cate- 
gorical Syllogism  in  which  there 
is  no  unnecessary  distribution 
of  terms  in  the  premisses.  Cf. 
Strengthened  Syllogism, 

Galenian  Figure  — The  fourth 
figure  of  Syllogism  is  sometimes 
so  called,  after  Galen,  who  is 
supposed  to  have  first  recog- 
nised it. 

General  Classification — Cf.  Classi- 
fication, Natural. 

Generalisation — The  change  in  a 
Term,  by  which  its  Application 
is  extended  or  widened  ;  the 
verb  to  boycott  is  a  recent  ex- 
ample.    Cf.  Specialisation. 

Generic — Relating  to,  or  belonging 
to,  a  Genus. 

(Jenus — A  class  considered  as  con- 
taining smaller  classes,  160,  161; 
one  of  the  Predicables,  Note  ii. 

Genus  Generalissimum — Cf.  Sum- 
mum  Genus. 

Proximate  (or  Proximum) — 

The  Proximate  Genus  of  any 
Class  is  the  next  wider  class  in 
which  it  is  contained,  160,  161, 
Note  II. 

,  Summum — The  widest  Class 


with  which  we  are  concerned  in 
any  given  case,  160, 161,  Note  ii. 

Heterogeneity,  Law  of — This 
Law  asserts  that  any  two  things, 
however  similar,  must  be  dis- 
similar or  heterogeneous  in  some 
respects.  This  is  equivalent  to 
Leibnitz's  principle  of  the  Id- 
entity of  Indiscernible s,  and  to 
one  of  the  Laws  of  Similarity 
given  on  pp.  147  and  207,  namely, 
that  'No  two  things  have  all 
characteristics  similar. ' 


S 


274 


INDEX   AND   VOCABULARY. 


Heterogeneous — Of  various  kinds. 

Heteropathic  Effect — A  Complex 
Effect  in  which  the  joint  effect 
is  different  from  the  sum  of  the 
separate  effects. 

Highest  Class  — Cf.  Summiim 
Genus. 

Homogeneity,  Law  of — This  Law 
asserts  that  the  most  dissimilar 
things  must  be  similar  (or  homo- 
geneous) in  some  respects.  It  is 
expressed  in  one  of  the  Laws  of 
Similarity  given  on  pp.  147  and 
207,  viz.  'No  two  things  have 
all  characteristics  different.' 

Homogeneous— Of  the  same  kind. 

Homonymous  Terms— The  same 
as  Amhi(juoHs  Terms. 

Hypothesis — Something  which  is 
supposed,  a  conception  or 
theory,  148. 

Hypothetical  Argument — 1 50, 1 52. 

HYPOTHETIGO  -ALTERNA- 
TIVE—CI.  I  n/ereutio- Alterna- 
tive. 

Hypothetico  -  Categorical  Argu- 
ment— 150,  152. 

Identical  —  Numerically  the 
same,  the  same  individual  — 
numero  tantum  (antithetic  to 
distinctf  other^  etc.). 

Identity— The  Numerical  Same- 
ness, or  continued  existence,  of 
one  thing  or  group  (antithetic  to 
Diatiiictnes.s^OtherneM — compare 
*  Mistaken  identity ')  20-25  pas- 
sim-, 29,  36,  41. 

Identity  in  Diversity,  20  seq.,  74, 
75,  203  se^.,  211. 

Law  of,  202,  etc.,  206,  207. 

Is  the  Principle  of  the 

possibility  of  significant  asser- 
tion, 209. 

■  Its  relation  to  Inference, 


75,  210,  211, 

Identity    of   Indiscernibles — The 

principle  recognised  by  Leibnitz, 

and   known   under   this   name. 


embodies  the  view  that  no  two 
things  can  be  alike  in  all  points 
(if  they  were,  how  should  we 
know  them  to  be  twot) — 207. 
Cf.  Law  of  Heterogeneity. 

Illation  =  Inference. 

Illative  =  Inferrible. 

Imperfect  Figures — Figures  2,  3, 
4  of  the  Categorical  Syllogism 
are  so  called. 

Inconsistent  Propositions.  Cf. 
Incompatible  Propositions. 

Indesignate  Propositions  —  Cate- 
gorical Class  -  Propositions,  of 
which  the  Subject  is  unquantitied 
(sometimes  called  'Indefinite'). 

Index  Classification — A  system- 
atic grouping  which  is  made  for 
purposes  of  reference — e.g.  the 
alphabetical  grouping  of  words 
in  a  dictionary,  or  an  ordinary 
book -index. 

Indiictio  per  Enumerationem  sim- 
plicem — Cf.  Induction  by  Simple 
Enumeration. 

Induction,  81-85,  87,  133-149. 

Meaning  of,  81. 

Justification  of,  1.35  stq. 

Mathematical,  141. 

Principle  of — Cf .  Principle  of 

Interdependence. 

Differentia  of,  147. 

Analysed,  145-146,  148. 

Practical  maxim  of,  147. 

by  Simple  Enumeration — An 


empirical  procedure,  in  which 
we  generalise  from  the  mere 
enumeration  of  one  or  more 
cases  to  a  universal  statement. 
Cf.  Empirical  Laiv. 

Inductive  Argument,  32,  Section 
xiii. 

' Syllogism,'  in  the  sense  of  a 

Syllogism  expressing  a  '  Perfect 
Induction.'     Cf.  Note  iii. 

Methods,  139-144. 

The   assumptions  on 


which  they  are  based,  144,  209 
210. 


INDEX   AND   VOCABULARY. 


275 


Inductive  Methods,   Their  func- 
tion, 210. 
Mill's  Canons  of— Note 

VI. 

Infer,  Inference,  Inferend,  Defini- 
tion of,  86. 
Inference   from   Whole   to   Parts 

and     from     Parts     to    Whole, 

74. 
Inferences,  31,  79-87. 
Definitions  of,  79,  85,  86,  88, 

114. 
Immediate  (Cf.    Eduction.^), 

79-80,  88-107. 

Mediate,  80-85,  114-156. 

IXFERENTIA  L      MEDIA  TE 

INFERENCES,  Definition  of, 

150. 

Division  of,  150,  152. 

Canons  of,  150-151. 


INFERENTIO-GATEGORI. 
GAL  ARGUMENTS  —  These 
include  Hypothetico-Categorical 
and  Conditio-Categorical  Argu- 
ments. 

INFERENTIG-ALTERNA- 
TIVE  ARGUMENTS,  153, 
etc.,  156. 

Intension — Cf .  Gonnotation . 

Intention,  Names  of  First  and 
Second — In  the  terminology  of 
Scholastic  Logic,  a  name  is  of  the 
First  Intention  if  it  is  the  simple 
directname  of  theobjectto  which 
I  apply  it.  E.g.  if  t  say  That  is 
a  cow,  cow,  as  so  used,  is  a 
term  of  First  Intention.  But 
if,  considering  the  logical  char- 
acter of  a  coic  in  the  above 
sentence,  I  say  that  it  is  a  Pre- 
dicate, or  a  Predicable,  then  I 
am  regarding  it  as  a  name  of 
Second  Intention. 

Interdependence,  135  sr^/. 

Principle  of,  135. 

Proof  of,  139  seq. 

Inter-relation,  Principles  of,  210- 
211. 

Inter-relation  of  things,  204,  etc. 


INTRA  VERSE,    INTRA  VER- 

SIGN,  90,  107. 
Inversions,    88,   97-98,    102,    105, 

107. 

Judgment— An  Assertion. 

Justification  may  be  described  as 
showing  that  a  thing  is  right,  or 
is  what  it  ought  to  be.  An  action 
is  exp)lained  if,  e.g.,  its  cause  is 
given  ;  it  is  justijied  if  it  is 
shown  to  be  right. 

Language,  Definition  and— 163- 
177. 

Growth  of ,  1 7 1  - 1 72.     - 

An  Ideal,  172. 

Ambiguity  of,  172-176. 

Law  of  Concomitance  of  Charac- 
teristics, 135,  209. 

of  Causation  of  Events,  135, 

209. 

of  Heterogeneity,  207. 

of  Homogeneity,  207. 


Likeness — Cf,  Similarity. 
Limitation,    Conversion   by — The 

Conversion  of  A  to  I  is  so  called. 

Cf.  Gonversioi  ^ler  Accidens. 
Logic,  Scope  of,  2,  3. 

Definition  of,  3. 

Assumptions  of,  .3. 

Lowest  Class — Cf .  Infima  Species. 
Lowest      Species  —  Cf.      Infima 

Species. 

Major  Term,  115. 

Illicit  Process  of,  119. 

Mathematical  Axioms,  206. 

Inductions,  141,  206. 

Mediate  Inference  (Argument), 
Definition  of,  114. 

Mediate  Inferences,  Inferential — 
Cf.  Inferential  Mediate  Infer- 
ences. 

Alternative — Cf.  Alternative 

Mediate  Inferences. 
Membra  Dividentia — Cf.  Go-ordi- 

nate  Glasses, 
'  Mental  Equivalents  '  of  Names, 

175-177. 


AMlfii  iTfiliifiiilhiirrillnli  ff 


276 


INDEX   AND   VOCABULARY. 


Metaphysical  Division — An  enu- 
meration of  the  co-inherent 
characteristics  of  any  object 
has  been  so  called.  E.(i.  A 
rose  may  be  '  metaphysically 
divided  '  into  colour,  form,  size, 
and  fragrance. 

Method,  157  f^cq. 

Rules  of,  157-158. 

Method  of  Discovery  —  Cf . 
Anab/sis. 

Method  of  Instruction — Cf.  Si/n- 

'  Methods  of  Experimental  In- 
quiry ' — This  is  the  name  given 
by  Mill  to  the  Methods  of  In- 
ductive research  formulated  by 
him  under  the  names  of  Method 
of  Agreement,  Joint  Method, 
Method  of  DitFerence,  Method 
of  Residues,  Method  of  Con- 
comitant Variations.  Mill's 
CanoiiH  of  these  methods  are 
given  in  Note  vi.  The  treat- 
ment of  Inductive  Methods  in 
Section  xiii.  differs  somewhat 
from  Mill's. 

Method  of  Agreement,  139,  140. 
Note  VI. 

in  Presence  and  Ab- 
sence, 1.39-140  (Joint  Method 
of  Agreement  and  Difference, 
Indirect  Method  of  Difference. 
Note  VI.). 

Method  of  Difference,  141-143. 
Note  VI. 

of  Residues,  143-144.  Notevi. 

of  Concomitant   Variations, 

144.  Note  VI. 

Middle  Term,  115. 

Absence  of,  118,  etc. 

Minor  Term,  115. 

Illicit  Process  of,  119. 

MIXED  ALTERNATIVE  AR- 
GUMENT, 153,  156. 

INFERENTIAL  ARGU- 
MENT, 150-152 

Mnemonic  Verses  {Barbara,  Ctl- 
arenty  etc.),  122,  123. 


Modal  Proposition  (as  distin- 
guished from  a  Pure  Proposi- 
tion) means  (1)  one  in  which 
the  Predicate  is  asserted  cum 
modo,  some  adverb  of  time, 
place,  manner,  etc.,  being  at- 
tached to  the  copula.  E.(j.  A 
is  alwayx  B,  X  is  generally  Y  ; 
(2)  A  Modal  Proposition  means 
one  in  which  there  is  an  ex- 
plicit indication  of  the  degree 
of  certainty  or  probability  with 
which  the  proposition  is  as- 
serted. E.g.  AisneceHnarily  B, 
X  is  pof/iildy  Y. 

Modus  Ponendo  Tollens  —  The 
mood  which  by  affirming  denies 
— the  form  of  Categorico- Alter- 
native Argument  in  which  the 
Minor  is  affirmative  and  the 
Conclusion  negative. 

Modus  Tollendo  Ponens,  the  mood 
which  by  denying  affirms— The 
form  of  Categorico-Alternative 
Argument  in  which  the  Minor 
is  negative  and  the  Conclusion 
affirmative.  This  is  not  a 
cogent  form  of  argument. 

Modus  Ponens— The  constructive 
form  of  Mixed  Inferential  Argu- 
ment, i.e.  that  in  which  Minor 
and  Conclusion  are  affirmative 
propositions.  The  Syllogism  on 
p.  50  and  the  third  Syllogism 
on  p.  49  are  of  this  form. 

Modus  Tollens— The  destructive 
form  of  Mixed  Inferential  Ar- 
gument, i.e.  that  in  which 
Minor  and  Conclusion  are  nega- 
tive.    Cf.  Modus  Ponens. 

Mood  and  Figure,  Importance  of 
Distinctions  of,  120-121. 

Mood,  Definition  of,  etc.,  121-122 
seq. 

Most,  meaning  of,  69. 

Name,  5. 

Distinguished    from    Term, 


5. 


INDEX   AND   VOCABULARY. 


277 


Name,  Definition  of,  5. 
Twofold   Function   of 


20. 


,  5, 


6, 


Distinctions  of,  10,  11. 

—  Divisions  of,  6,  9,  12. 

—  Table  of,  18. 

—  Common,  12. 

—  Proper,  6,  7, 12. 

—  MIXED,  7. 

—  INDIVIDUAL,  7,  8. 

—  ATTRIBUTE,  11,  16. 

—  SPECIAL,  8,  12. 

-  SUBSTANTIVE,  12. 
UNIQUE,  12. 


Natural  Classification— Cf.  Classi- 
fication, Ai'tijicial. 

'  Natural  Group'  (or  '  Real  Kind') 
— Applied  by  Mill  to  '  those 
classes  which  are  distinguished 
from  all  others,  not  by  one  or  a 
few  definite  properties,  but  by 
an  unknown  multitude  of  them ; 
the  combination  of  properties 
on  which  the  class  is  grounded 
being  a  mere  index  to  an  in- 
definite number  of  other  dis- 
tinctive attributes.'  (It  might 
be  maintained  that  this  account 
would  apply  to  every  class.) 
egative  Instances  —  Cf.  224, 
Canon  of  Joint  Method  of  Agree- 
ment and  Difference — '  instances 
in  w^hich  the  phenomenon  does 
not  occur. ' 

Negative  Terms — A  Term  with  a 
negative  meaning,  or  negative 
prefix,  is  called  Negativ^e.  When 
two  correlated  terms  are  nega- 
tives of  each  other  they  are  re- 
lated as  B  and  not-B.  E.g. 
White,  not-  White  are  correlated 
negatives. 

Nomenclature  —  A  Collection  of 
Names  of  the  distinct  objects 
and  classes  which  are  treated  of 
in  any  science.  E.g.  Roses, 
Dandelions,  Oaks,  Beeches,  are 
part  of  the  Nomenclature  of 
Botany. 


Nominalist  Doctrine  of  General 
Names — On  this  view  there  is  no 
Real  Universal  corresponding 
to  General  Names  (as  on  the 
Realist  Hypothesis),  and  no 
General  Notion  in  the  mind  (as 
on  the  Conceptualist  View)  ;  but 
the  only  generality  in  the  case 
is  the  general  application  of  the 
name  itself  to  the  particular 
individuals  which  are  called  by 
the  name. 

Observation  means  simply  watch- 
ing, noting,  or  taking  account 
of  ;  it  is  often  used  in  the  special 
sense  of  Scientific  Observation 
— that  is,  Observation  for  pur- 
poses of  Science. 

Obverse — The  Proposition  reached 
by  Obversion. 

Obversions,  88, 91-93, 100, 103, 107. 

Obvert — To  perform  the  process  of 
Obversion. 

Obvertend — The  Proposition  to 
be  obverted. 

Opposite  (or  Contrary)  Terms — 
When  two  terms  have  the  most 
extremely  opposite  meaning 
possible,  they  are  called  Op- 
posite or  Contrary,  e.g.  Black 
and  White.  Compare  Negative 
Terms. 

'  Opposition '  of  Propositions — 
Note  I. 

Square  of — Note  i. 

Ostensive  (or  Direct)  Reduction, 
124. 

OTHERNESS  (-Distinctness), 
20,  23-25,  29. 

P — used  for  Predicate  of  a  Cate- 
gorical Proposition,  9,  24,  etc. 

Paradox — A  Statement  contrary 
to  common  opinion. 

Parallelogram  of  Forces — Note  v. 

Paralogism — A  '  Logical '  or  For- 
mal Fallacy. 

Parcimony,  Law  of — asserts  that 


278 


INDEX   AND   VOCABULARY. 


*  we  ought  always  to  make  as  few 
assumptions  as  possible.' 

Partition  or  Physical  Division — 
Distinguishing  a  material  object 
into  its  parts — e.g.  a  violet-plant 
into  root,  stalks,  leaves,  and 
flowers. 

Perfect  Figure — Figure  I.  of  the 
Categorical  Syllogism,  123. 

'  Perfect  Induction  ' — Note  iii. 

Permutation — Same  as  Obversion. 

Phenomenon  —  Anything  (simple 
or  complex)  which  appears  or 
is  apprehended. 

Plurality  of  Causes — The  doctrine 
of  Plurality  of  Causes  implies 
that  different  kinds  of  cause 
may  produce  the  same  kind  of 
effect.  This  view  can  be  ac- 
cepted as  plausible,  only  if  )<ame 
effect  is  taken  in  a  looser  sense 
than  same  cau>>e  ;  as  e.q.  when 
it  is  said  that  different  cause.^ 
— such  as  poison,  violence,  acci- 
dent or  disease — may  produce 
the  same  effect,  namely  Death. 

Plurative  Proposition — A  Pro- 
position of  which  the  Subject  is 
quantified  by  a  definite  number, 
e.f/.  Six  ^'s  are  B,  hK  is  M. 

Polylemma  (Tri-lemma,  Tetra- 
lemma,  etc.) — An  Argument  of 
the  same  form  as  a  Di-lemma, 
but  which  has  more  than  two 
Alternatives. 

PON  END  A  L  TERN  A  TI VE 
ARGUMENTS,  154,  156. 

Porphyry — Note  it. 

Tree  of — Note  ii. 

Positive  Term — One  which  is  not 
negative  in  form  or  meaning. 

Postulate — '  A  position  or  a  pro- 
position of  which  the  truth  is 
demanded  or  assumed  for  the 
purpose  of  future  reasoning ;  a 
supposition'  (Worcester's  Dic- 
tionary of  the  English  Language). 
E.g.  in  geometry, '  if  you  will  not 
allow   me  to  describe  a  circle 


whenever  I  desire,  then  I  can- 
not make  one  line  the  same 
length  as  another.  .  .  ,  Thus 
the  postulates  are  the  conditions 
of  .  .  .  reasoning,  but  them- 
selves form  no  part  of  the  reason- 
ing '  (A.  Milnes). 

Predicables — Note  ii. 

Predicamental  Line — Note  ii. 

Predicate,  9. 

Premiss,  73,  115. 

Major,  115. 

Minor,  115. 

Premisses,  Defined,  86. 

Principle  of  Categorical  Assertion 
— Cf.  Lav  of  Identity  in 
Dirersity,  202,  etc. 

Principle  of  Interdependence, 
135,  206,  207,  209. 

Principles  of  Logic,  202-211. 

Privative  Conception,  Inference 
by — Same  as  Obversion. 

Proper  Names,  6-7,  163-164,  166- 
167,  173-174. 

Proposition,    Definition    of,    1, 
4. 

Division  of,  4. 

Import  of,  4,  20,  etc. 

Relative  and  Absolute,    14, 

etc. 

CATEOORirvL,  4,  20-33. 

Analysis  of,  5,  8,  9,  20- 

25,  27-29,  36. 

Symbolic  representation 


of,  9. 

— Definition  of,  20. 

Import  of,  20  seq. 

(Classification  of,  30-33. 

Division    of — Cf.    Cla.'i- 

sijicafion  of. 

Whole,  30,  33. 

Partial   or   l\articular. 


30,  33. 


33. 


ATTRIBUTE,    30, 


PROPER,  30,  33. 
UNIQUE,  30,  33. 
SPECIAL,  30,  33. 
COMMON,  30,  33. 


INDEX   AND   VOCABULARY. 


279 


Propositiox,  Universal  and  Gene- 
ral, 30,  31,  32. 

Definite  and  Indefinite,  30, 

31. 

RELATIVE   and    ABSO- 
LUTE, 30,  31. 

Distributive  and  Collective, 


30,  31. 

Affirmative    and    Negative, 


31,  etc. 
—  ADJECTIVAL,  14. 

cannot  be  cjuantificated 


or  converted,  15. 

—  COINCIDENTAL,  14,  15. 

—  Class,  25,  26. 
INFERENTIAL,  4,  42-50, 


51,  99-103,  112. 

Definition  of,  42. 

—  Division  of,  42,  51. 

Forms  of,  42. 


—  Conditional   (Cf.    Inferen- 
tial), 4,  42,  43-44,  49,  50. 

Definition  of,  43. 

Division  of,  47,  48,  51. 

Analysis  of,  47,  48. 


—  DIVISIONAL,  47,  51, 

—  QUASI-DIVISIONAL,  47- 
48,  51. 

Hypothetical,  4,  42,  43, 44- 


CONTAINED,  45,  51. 

REFERENTIAL,  45- 


DO. 


47,  51. 

Whately's  Definition  of, 

ALTERNATIVE  (or  Dis- 
junctive), 4,  52-56,  57,  103-105, 
112-113. 

Definition  of,  5o. 

Forms  of,  52,  53. 

-  Division    of,    53,    54, 


57. 


CONDITIONAL,  53, 


Oi. 


PROPOSITION,  ALTERNA- 
TIVE, FORMAL  or  SELF- 
CONTAINED,  53,  54,  57. 

SUBSUMPTIONAL, 

53  54  57. 

'-CONTINGENT,  54, 57. 


— Disjunctive— Cf.  Alternative. 

—  Compound,  109. 

—  Relations  of,  72-77,  78,  157, 
158, 159,  etc.  Cf.  Inferences,  In- 
compatible Propositions,  Ijiduc- 
tions.  Fallacies,  Division,  etc. 

—  ATTACHED,  72-74. 

—  UNATTACHED,  74,  78. 

—  Compatible,  72,  78. 

—  Incompatible,  72,  78, 108-113. 
Definition  of,  72,  108. 


—  CORRELATIVE,  72,  78. 

—  Contrary  and  Contradictory 
— Cf.  Incompatible  Propositions. 

—  Sub-contrary,  72,  78. 

—  PREMISSAL—12,  78. 

—  ARGUMENTAL,  Relation 
between,  73,  78. 

CLASSIFIC,  Relation   be- 


tween, 73-74,  78,  109. 
—  Mathematical,  14,  37-41. 
0  not  convertible,  15,  65-66 


/  7 7 7 

47,  49,  51.     Cf.  also  Inferential 

Proposition. 

Definition  of,  44. 

Division  of,  45,  51. 

Analysis  of,  45-47. 

-  FORMAL  or   SELF-    \ 


Proprium  (Property) — Note  ii. 

Pro-Syllogism — Note  rv. 

PURE  ALTERNATIVE  AR- 
GUMENTS, 153,  156. 

PURE  INFERENTIAL  AR- 
GUMENTS, 150,  152. 

Quality  of  Propositions— Their 
affirmativeness  or  negativeness. 

Quantification,  Meaning  of,  58 
note. 

Function  of,  69. 

Quantification  and  Conversion, 
58-66. 

QUANTIFICATE— To  quantify 
the  Predicate-Name,  58. 

Quantify — To  add  some  adjective 
of  quantity  to  the  Subject- 
name  or  Predicate-name  of  a 
Proposition,  5,  58. 

Quantitative      Induction — Deter- 


280 


INDEX   AND   VOCABULARY. 


minatiou,  by  Induction,  of  the 
quantity  of  any  factor  involved. 
The  Methods  of  Concomitant 
V^ariations  and  of  Residues  are 
sometimes  called  Methods  of 
Quantitative  Induction. 

Quantity  of  Propositions — their 
Universality  (Generality)  or 
Particularity. 

QUASI-CATEGORICAL  —  De- 
noting a  combination  of  words 
akin  to  a  Categorical  Proposition 
— e.g.  the  Antecedent  of  a  Con- 
ditional Alternative — 53,  etc. 

Quattrnio  Termiuoruin—The  fault 
of  four  Term-names  in  Premisses 
and  Conclusion  of  a  Categorical 
Syllogism. 

Question-begging  Epithets,  178. 

Ramean  TREE-Cf.  Tree  of  Por- 
phjry. 

Ramus — Note  ii. 

Ratiocination — Note  v. 

Realist  Hypothesis  of  Universals 
— Note  II. 

Real  Proposition — Cf.  Ampliativt 
Pro2toxition. 

Reduction — the  process  of  chang- 
ing a  Categorical  Syllogism 
from  Fig.  2,  8,  or  4,  to  Fig.  1  ; 
more  generally,  the  process  of 
changing  an  argument  from  one 
mood  to  another,  123  -^tq. 

Direct  (or  Ostensive),   125- 

127,  129. 

Indirect  {Reductio  ad  imjws- 


sibile,  Reductio  ad  ab.surdum,  Re 

duct >o  per  impossihile),  127-128. 
Relation  between  Classes,  25. 

Terms,  25. 

Propositions,  72-78,  etc. 

Residues,  Method  oi—Cf.  Method 

of  Residues. 
Residual  Phenomena — Phenomena 

that  remain  unaccounted  for  in 

an  investigation. 
RETROVERSION,  88,  97,  102, 

105,  107. 


REVERSE,  REVERSION,  90, 
107. 

S — used  for  Subject  of  a  Cate- 
gorical Projionition,  9,  24,  etc. 

Sameness — (1)  Identity,  or  (2) 
Similarity — (antithetic  to  Dif- 
ference). 

Secundi  adjacentix,  '  of  the  second 
adjacent ' — Applied  to  a  Cate- 
gorical statement  consisting  of 
(1)  Subject  (2)  Verb — e.g.  Rem- 
brandt paints. 

Self-evidence,  Principle  of,  3,  211. 

Self-evident  —  A  Proposition  is 
called  self-evident  if,  when  it  is 
understood,  '  it  is  very  clearly 
and  distinctly  seen  to  be  true,' 
and  that  without  dependence 
upon  any  other  Propositions. 

Signification  of  Names  and  Terms, 
5,  6,  20,  \6S-i:7 pa.^sim. 

Statement  of,  1G3. 

Rules  for  determining,  1C9- 

170. 

Similarity — There  is  similarity 
between  tico  things  when  they 
resemble  each  other,  produce 
impressions  which  we  call  like  ; 
and  there  is  similarity  between 
the  different  phases  of  one  thing 
in  as  far  as  it  remains  unaltered. 
Similarity  may  be  slight  and 
partial,  or  so  great  as  to  amount 
to  what  has  been  called  indis- 
tinguishable resemblance  {sjyecie 
tantum).  Similarity  (Resem- 
blance) is  antithetic  to  Diversity 
— 205,  etc. 

and  Dissimilarity,    Maxims 

of,  138,  147,  207,  209. 

in   Otherness   (or   Distinct- 


ness), 20sc(/.,  73,  74,  211. 

Some,  66-69. 

Definition  of,  68. 

Sophism  —  A  specious  but  fal- 
lacious Argument,  which  may 
or  may  not  be  used  with  intent 
to  deceive. 


' 


1 


INDEX    AND   VOCABULARY. 


281 


Sorites — Note  iv. 

Progressive — Note  iv, 

Regressive   or    Goclenian — 

Note  IV. 
Special  Classification — Cf.   Classi- 
fication, A  rtifria  I. 
Specialisation — The   change  in    a 
term  by  which  its  application  is 
narrowed  or  restricted— e.r/.  the 
word  Speaker  is  specialisedVhen 
used  to  indicate  the  chairman 
of  the  House  of  Commons.     Cf. 
Generalisation. 
Species  (Predicable) — Note  ii. 

,  Infima — Note  ii. 

Pra^diccdjilis — Note  ii. 

'  Subjicibilis — Note  ii. 

Statement,  Definition  of,  1 . 
Strengthened  Syllogism—A  Cate- 
gorical   Syllogism     which    has 
more  terms  distributed  in  the 
Premisses  than  is  necessary  in 
order  to  justify  the  conclusion. 
Darapti,      Felapton,      Fesapo, 
Bramantip     are     strengthened 
Syllogisms, 
Sub-altern — Note  i. 
Subalternation,  67,  8S,  93,  107. 
Subaltern  Genera  and  Species- 
Note  II. 
Subalternans,     Subalternate  —  A 
and  E  is  each  a  Subalternans  to 
I  and  O  respectively  ;  I  and  O 
are  Subalternates  to  A  and  p]. 
Sub-contrary— O  and   I  Proposi- 
tions are  said  to  be  Sub-contrary 
to  each  other — Note  i. 
Subject,  9. 
SUBVERSION,    88,   93,    95,   96 

note,  100-101,  104,  107. 
Sufficient  Reason,  Law  of— as- 
serts that  Nothing  can  he  or 
happen  without  an  adequate 
reason  of  its  being  or  happening. 
Sui  generis— oi  its  own  kind,  i.e. 

unique. 
Sumption    (1),   Subsumption  (2); 
Sir  William  Hamilton's  names 
for  the  Major  Premiss  (1)  and 


the  Minor  Premiss  (2)  of  a  Cate- 
gorical Syllogism. 
Suppositio  Materialis—'  There  is 
a  sense  in  which  every  word  may 
become  categorematic,  namely, 
when  it  is  used  simply  as  a 
word,  to  the  neglect  of  its  proper 
meaning.  Tlius  we  can  say 
' '  Swiftly  is  an  adverb. "  Su-iftly 
in  this  sense  is  really  no  more 
than  the  proper  name  for  a  par- 
ticular word.  This  sense  is 
technically  known  as  the  Sup- 
positis  Materialis  of  a  word ' 
(Stock,  Deductive  Logic,  section 
/O). 

Syllogism  (Absolute  Argument). 

Categorical,  114-129. 

Defined,  114. 

Analysed,  115. 

Hypothetical  and  Condi- 
tional, 49,  50,  150-152. 

SYLLOGISMS,  ALTERNA  - 
TIVE—Ct  Alternative  Mediate 
Inferences, 

SYLLOGISMS,  INFEREN- 
TIAL—Qi.  Inferential  Mediate 
Inferences. 

Symbolic  Logic— This  phrase  is 
ordinarily  used  to  designate 
'  that  branch  of  the  science  in 
which  symbols  of  operation  are 
used.  Of  course  in  one  sense, 
all  Formal  [  =  General]  Logic  is 
symbolic '  (Dr.  Keynes). 

Syncategorematic  (pp.  85,  86)— A 
word  is  Syncategorematic  if  it 
cannot  stand  as  the  Subject  or 
Predicate  of  a  Categorical  Pro- 
position. 

Synthesis— The  operation  of  build- 
ing up  parts  into  a  whole  (cf. 
Analysis).  The  Method  of 
Synthesis  is  said  to  be  a  Method 
of  Instruction,  because  it  is 
largely  used  in  the  teaching  of 
subjects  (such  as  Mathematics) 
in  which  the  laws  and  principles 
have  been  already  discovered, 


■^i^a^^^S^ 


2.S2 


INDEX   AND   VOCABULARY. 


and  the  pupil  is  instructed  how 

to  combine  and  apply  them. 
Synthetic   Proposition— Cf.   Am- 

pliative  Proposition. 
System — By   St/stem  is   meant    a 

group  of  two  or  more  related 

objects. 
Systematisation,  159,  102. 

Tautology,  110,  etc. 

Tautologous  Proposition — A  Pro- 
position of  the  forms  (1)  ^4  is  A, 
(2)  I/A,  then  A,  or  {3)  A  or  A. 

Tkrms,  5-17,  19. 

Distinguished  from  Name,  5. 

Definition  of,  9, 

Distinguished  from  Term- 
name,  10. 

Division  of,  13,  15,  1(). 

Dependence  of,  on  Context, 

12,  13,  172  seq. 

Table  of,  19. 

UNI-TERMINAL,  13,  14, 


15. 

BI-TERMIXAL,  13,  14,  15. 

Universal  and  General,  12. 

Whole,  15,  16. 

Partial,  15,  16. 

UNIQUE,  15. 

PROPER,  15. 

Common,  15. 

SPECIAL,  15. 

Relative,  13,  14.  15. 

Absolute,  13,  14,  16. 

Definite,  16. 

Indefinite,  1(5. 

ATTRinUTK,  15. 

SUBSTAXTLVE,  15. 

Technical,  16. 

Application   of,    30,   Section 

iii.  passim. 
Signification  of,  36,  Section 

iii.  passim. 
TERM-CONSTITUENT  —   A 

Term-Name  or  Term-Indicator. 
TERM-INDICA  TOR,  10, 64, 178. 
TERM-NAME,  10,  115,  178. 

and  Term,  distinguished,  10. 

Terminology — has     been     distin- 


guished from  Nomenclature,  as 
including  all  the  terms  neces- 
sary to  describe  the  oljjects 
referred  to  by  the  names  which 
come  under  the  head  of  Nomen- 
clature— e.ij.  petal,  calyx,  co- 
rolla, are  part  of  the  terminology 
of  Botany.  It  is  sometimes 
difficult  to  distinguish  between 
Nomenclature  and  Terminology 
— e.g.  to  say  under  which  head 
Terms  and  Propositions  ought 
to  be  classed,  in  Logic. 

Tertii  Adjacentis,  'of  the  third 
adjacent ' — applied  to  a  Catego- 
rical Statement  consisting  of 
(1)  Subject,  (2)  Copula,  (3) 
Predicate — e.g.  Rembrandt  is 
painting. 

Things,  Two-fold  aspect  of,  5,  6, 
20 

TOLLEND  ALTERNATIVE 
ARGUMENTS,  154,  156. 

Totnni  Divisum— The  whole  which 
is  separated  intoparts — Membra 
Diridentia — by  division. 

Traduction— This  term  is  apj)lied 
by  Jevons  to  Categorical  Argu- 
ments in  which  all  the  Subjects 
have  identical  application — e.g. 
Snowdon  is  the  highest  hill  in 
Wales  ;  Snowdon  is  not  so  high 
as  Ben  Nevis  ;  .  *.  the  highest 
hill  in  Wales  is  not  so  high  as 

TRANSFORMATIONS,   98-99, 

103,  105,  107. 
TRANS  VERSIONS,  88, 105-106, 

107. 

Undistributed  Term — Cf.  Dis- 
tributed Term. 

Uniformity,  135  .se^. 

Uniformity  of  Interdependence, 
204,  205,  205  note. 

Uniformity  of  Succession — depen- 
dent upon  uniformity  of  Co- 
existence, 137.— The  principle 
of  Uniformity  of  Succession  (oi- 


INDEX    AND    VOCABirLAKV 


2S:^ 


(.■ausation)  is  formulated  as 
follows  by  the  late  Professor 
Clerk  Maxwell,  under  the  name 
of  'The  General  Maxim  of 
Physical  Science  ':— 'The  difler- 
ence  between  one  event  and 
another  does  not  depend  on  the 
mere  difference  of  the  times  or 
the  places  at  which  they  occur, 
but  only  on  differences  in  the 
nature,  configuration,  or  motion 
of  the  bodies  concerned. '  (Cf. 
Cavse  and  Effect.) 

Unity  in  Difference— 73,  75,  etc. 

,  the    three     kinds     of.    75, 

211. 

Univocal  Name— A  Name  which 


has  only  one  application — con- 
trasted with  Equji'oval  Nam^', 
172. 

Vjirbai.  Pjioposition— Cf.  Essen- 
fiat  /Proposition. 

Verification— Proof  by  appeal  to 
experience,  Note  v. 

Weakened  Syllogism— A  Cate- 
gorical Syllogism  in  which  the 
Conclusion  is  Particular  when 
the  Premisses  would  justify  its 
being  Universal.  A  Weakened 
Syllogism  has  a  Weakened  Con- 
clusion, and  is  said  to  be  in  a 
Subaltern  Mood. 

Whole  and  Parts,  74,  75. 


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